# how to find area of rectangle with diagonal and width

the width (W) is shorter than the length and in this case the width is 8 and the length is 6.. How do I find the area of a rectangle if width and perimeter are given? We use cookies to make wikiHow great. 2. In the figure at the top of the page, click on 'reset' and 'hide details'. I tried solving this problem using trigonometry since diagonal and two sides forms a right triangle, from area i got that a=168/b, considering that area is a*b=168, I reached to a quadratic equation but i … So the valid solution is the one in which we found the length is 8 and the width is 6.. Just as a check we can add 8 + 6 + 8 + 6 and find that the perimeter is 28, as the problem said it should be. There are numerous ways to find a missing dimension of a rectangle, and the method you use will depend on what information you already have. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. http://www.coolmath.com/reference/rectangles#The_area_of_a_rectangle, http://www.mathopenref.com/rectanglearea.html, http://www.virtualnerd.com/middle-math/geometry-measurement/rectangle-perimeter-area/rectangle-perimeter-example, http://www.mathopenref.com/rectangleperimeter.html, http://www.coolmath.com/reference/rectangles#The_diagonal_of_a_rectangle, http://www.mathopenref.com/rectanglediagonals.html, http://www.algebralab.org/Word/Word.aspx?file=Geometry_AreaPerimeterRectangles.xml, http://www.algebralab.org/Word/Word.aspx?file=Geometry_AreaPerimeterRectangles, आयत की चौड़ाई पता करें (Find the Width of a Rectangle), consider supporting our work with a contribution to wikiHow. Let l and w be the length and width respectively. Rectangle is a two dimensional plane or geometric shape with 4 straight sides and 4 right angle (90º) corners. A rectangle with diagonal of 20 cm has sides in the ratio 2:1. You can use Pythagoras' theorem to find the diagonal from the length and width of the rectangle: d^2 = … share | cite | improve this question | follow | edited Sep 25 '19 at 16:29. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. If the side = 48 meters and the diagonal = 50 meters, how do I find the area of the rectangle? The formulas for the perimeter P, area A and length D of the diagonal of a rectangle of length L and width W are given by: P … If you don’t have the area, you can use the rectangle’s perimeter instead. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. And we can apply the Pythagorean theorem:.. The area of the rectangle = (2x+4)(x+5) = 2x^2+14x+20 = 2(x^2+7x+10). To find the area of a rectangle, multiply the length by the width. Subtract 10 from both sides: w² + 2w - 8 = 0. Amid the current public health and economic crises, when the world is shifting dramatically and we are all learning and adapting to changes in daily life, people need wikiHow more than ever. K-12 students may refer the below formulas of rectangle to know what are all the input parameters are being used to find the area, perimeter, diagonal, length or side of a rectangle. asked Sep 25 '19 at 16:20. right? C++ Examples. From the first equation, x = 40/y. All tip submissions are carefully reviewed before being published, This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Things to try. Just plug the area and length of the rectangle into the formula and solve for the width. The diagonals of the rectangle divide it into two equivalent right-angled triangles. The area of a rectangle is length times width. The area of the rectangle is 45 m 2. If the diagonal length of a rectangle is 19cm and the area is 120cm. To learn how to find the width of a rectangle using the diagonal and the length, scroll down! You could multiply the height and the length with each other first before dividing. K-12 students may refer the below formulas of rectangle to know what are all the input parameters are being used to find the area, perimeter, diagonal, length or side of a rectangle. In case you select to solve for area (A) you have to provide the length (l) and the width (w) then: If you want to calculate the perimeter (P) you have to input the length (l) and the width (w): In case you try to compute the diagonal of the rectangle (d) then you have to input the same two figures (its length and width… A square always has equal lengths. Using this calculator, we will understand the algorithm of how to find the perimeter, area and diagonal length of a rectangle. To find the width of a rectangle, use the formula: area = length × width. In Example 1, we found the area given the dimensions of the rectangle. Area = $$\sqrt{Diagonal^2 – Width^2}$$ × Width. Last Updated: December 3, 2020 Find the width of the rectangle and use the animation or the calculator above to verify your answer. Write an equation in B, stating that the perimeter is equal to twice the breadth plus twice the length. Let x and y be the dimensions of the rectangle. How would I find width when I've been given volume, height, and length? By the Pythagorean theorem, (w²) + (w+2)² = (√20)². If a and b are the sides, and d is the diagonal, the Pythagorean theorem states that. References. An easy to use online calculator to calculate the area, perimeter and diagonal of a area A and perimeter P of a rectangle given its dimensions (length and width). The length L of a rectangle is decreasing at a rate of 6 cm/sec while the width w is increasing at a rate of 6 cm/sec. Your support helps wikiHow to create more in-depth illustrated articles and videos and to share our trusted brand of instructional content with millions of people all over the world. width (a) = height (b) = diagonal (d) = alpha (α) = beta (β) = Round to decimal places. Plug the perimeter and the length into the formula and solve for the width. If a rectangle measures 2(3x - 1) cm by (2x + 3) cm, and its perimeter is 98 cm, what are its dimensions? The diagonal of a rectangle is the hypotenuse of the rectangle's width and height. How to find the area with diagonal of rectangle and width Formula: Area = $$Width\ \sqrt{(Diagonal^2 – Width^2)}$$ Find a missing side length when the area is known Formula: Length = Area/Width. You don't have enough information to solve. If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. And we can apply the Pythagorean theorem:.. Double the width, and subtract that from the perimeter. Considering pythogoras theorem this diagonal is the hypothenuse, which is the longest side of the triangle while the width becomes one side of the triangle. This article has been viewed 464,105 times. This means that the product of the length and width must be greater than 18. To find the area of a rectangle, multiply the length by the width. We know that, Area of rectangle (A) = width√ diagonal 2-width 2. You can use the Pythagorean Theorem because you’re working with a right angle triangle. This method will only work if you are given the length of the diagonal and the length of the side of the rectangle. … References. If I am given the area and width, how do I get the length? For example, a garden shaped as a rectangle with a length of 10 yards and width of 3 yards has an area of 10 x 3 = 30 square yards. Multiply the length of the rectangle by its width to find the area of the rectangle, and use the formula , where is the base and is the height of the triangle, to find the area of the triangle. When you’re working with rectangles, you can find out a lot of information about them just by knowing a few key points of information. So this rectangle is divided into 2 right angled triangles(90 degrees each). Mark the diagonal on the rectangle. To find the area of a rectangle you should multiply its length by its width. wikiHow is where trusted research and expert knowledge come together. The length of a rectangle field is twice its breadth. Therefore the two sides are 7" and 24" Then the area is: 7" x 24" = 168 square inches, or 168 square units STEP 3: Think of the possible dimensions the rectangle can have if the sum of the length and width equals 9 cm. wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article is backed by trusted research and meets our high quality standards. Then drag the corners to create an arbitrary rectangle. Always use a calculator to check your math, and don’t forget to add your units onto the answer! Thus √5 : 20 = 2 : x, where x is the longer side. In the figure at the top of the page, click on 'reset' and 'hide details'. To learn how to find the width of a rectangle using the diagonal and the length, scroll down! Dividing by √5: x = 40 / √5 = 40 / 2.236 = 17.9 cm. When diagonal and width is given. Is it possible to find the width and length of a rectangle by just know the diagonal? (3 in) A = 18 in 2. The ratio of √5 to the diagonal (20) is equal to the ratio of 2 to the longer side (or the ratio of 1 to the shorter side). How can I calculate the length and width of a rectangle if I am given the area? Finding Length and Width When You Know Area and Perimeter If you happen to know the distance around the rectangle, which is its perimeter, you can solve a pair of equations for L and W. The first equation is that for area, To find the width of a rectangle, use the formula: area = length × width. Using the Pythagorean theorem: w 2 … Use our online diagonal of a rectangle calculator to find diagonal of rectangle by entering the width and height. Subtract 14y from both sides to get zero on one side, and re-arrange slightly: y² - 14y + 40 = 0. Below are some special formulas related to the rectangle area. How to use the calculator Enter the perimeter P and area A as positive real numbers and press "enter". All tip submissions are carefully reviewed before being published, This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. The diagonal of rectangle is 25, its area is 168, find width and length. We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. The length of a rectangle is 2 inches more than the width. Like if the diagonal was 25, what would be the side lengths? Its shorter side is 4 less than its diagonal. According to the Pythagorean theorem, the diagonal value can be found knowing the side length. Calculator Enter 2 values. You cannot find length and width if all you're given is area. The formula is: A = L x W. where A is the area, L is the length, W is the width, and X means multiply . ; Calculating the area and perimeter is straight forward. the width (W) is shorter than the length and in this case the width is 8 and the length is 6.. In that case, you would use the formula: perimeter = 2 × length plus 2 × width. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. W = V / (H*L). Then (by the Pythagorean Theorem) s² + 48² = 50². Then drag the corners to create an arbitrary rectangle.Calculate the length of the diagonals.Click 'show details' to verify your answer. Example 2: Find the area of a rectangular board whose diagonal length is 20 cm and width is 13 cm. To find the diagonal, square the width and height of the rectangle and add the squared values. Round your answer to two decimal places. Explanation: . Area A = Perimeter P = Rectangle. You can solve by substitution from here -- you'll get a quartic, but it's really a quadratic in l^2 (or w^2 if you substitute the other way) so you can still solve it. Include your email address to get a message when this question is answered. Click 'show details' to verify your answer. Let B equal the breadth. 1) Diagonal = 2) Diagonal = 12 in 20 in 8 yd 19 ft t Area = 390.69 in" 24 in Area = 48 yd" Printable Math Worksheets @ www.mathworksheets4kids.com Name : Sheet 1 Answer key Area of a Rectangle A) Find the area of each rectangle for the given measurements. In this rectangle one of the sides is the height, which coincides with the length of the edge. Rectangle is two dimensional shape in geometry. According to the Pythagorean theorem, the diagonal value can be found knowing the side length. Your support helps wikiHow to create more in-depth illustrated articles and videos and to share our trusted brand of instructional content with millions of people all over the world. How do I find the length and breadth? Then solve for the width. Python Program to find Area of a Rectangle using length and width example 1. Find the area of the rectangle below that has a diagonal of 26 and length of 24. Then xy = 40, and 2x + 2y = 28. The diagonal of a rectangle divides it into two congruent right triangles. Your expression for the length is then, For example, if you know that area is 24 square centimeters, and that. By simply inputting the length and width, this calculator will almost instantly find the perimeter (P) and the area (A). To understand this example perfectly you should have the following C++ programming knowledge. The width of the rectangle is stored in the variable width and height is stored in the variable height. Rectangle: The formula for calculating the perimeter of a rectangle is P = 2(l+w) where l is length and w is its width. The formula is: A = L x W. where A is the area, L is the length, W is the width, and X means multiply Find the length of the diagonal, if the width is 6 feet. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a0\/Find-the-Area-of-a-Rectangle-Using-the-Diagonal-Step-1.jpg\/v4-460px-Find-the-Area-of-a-Rectangle-Using-the-Diagonal-Step-1.jpg","bigUrl":"\/images\/thumb\/a\/a0\/Find-the-Area-of-a-Rectangle-Using-the-Diagonal-Step-1.jpg\/aid5839965-v4-728px-Find-the-Area-of-a-Rectangle-Using-the-Diagonal-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

\u00a9 2020 wikiHow, Inc. All rights reserved. If x = 1, the figure is a square. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. So s² + 2304 = 2500. From there The area of a rectangle is height * width, so 10 * 24 = 240. Then these equations are solved for L and W which are the length and width of the rectangle. previous article. If interested in calculators for a variety of other shapes, you can look at more of our handy calculators. By using our site, you agree to our. It this case you first should use the Pythagorean theorem to find the another side. This image may not be used by other entities without the express written consent of wikiHow, Inc.
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\u00a9 2020 wikiHow, Inc. All rights reserved. In Example 1, we found the area given the dimensions of the rectangle. Find area of rectangle when given perimeter and diagonal I was helping my niece (going into 10th) with summer math, and am stumped. Then 2B equals the length. Finding area from a diagonal and vice-versa. Then s² = 196, and s = 14 m. The area is 48 x 14 = 672 square meters. In Part B, find the missing side using the area and the side provided and then find the diagonal using the theorem. Multiply both sides of this equation by y to get rid of the denominator: 80 + 2y² = 28y. That means that one side of the rectangle is 4 inches in length, and the other side is 10 inches. So l+w = sqrt(601) and l-w = 11. This image may not be used by other entities without the express written consent of wikiHow, Inc.
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\u00a9 2020 wikiHow, Inc. All rights reserved. I tried solving this problem using trigonometry since diagonal and two sides forms a right triangle, from area i got that a=168/b, considering that area is a*b=168, I reached to a quadratic equation but i … Please consider making a contribution to wikiHow today. X squared = 625 - 41 = 584. You divide the volume by the height and the length. Using those two values, it finds the area of a rectangle. Just plug the area and length of the rectangle into the formula and solve for the width. X = 24. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. Use either equation to solve for l in terms of w, or vice versa, then substitute that value of l into the other equation. This Python program allows user to enter the length and width of a rectangle. Part A contains the diagonal and the measure of one side. Rectangle has 4 sides and 4 corners. Example: find the area of a rectangle. That will give you the value of w. Use it in either equation to find the value of l. One side of a square chessboard is 75 cm; how would I find the area of the board? This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. If all you know is the length of the diagonal, you can calculate the area of a square, but not a rectangle. The relationship might be given by stating how many times bigger one side is than the other, or how many units more or less it is. In a rectangle, there are 4 vertices and 2 diagonals of congruent length. If you have have a rectangle of a given perimeter and want to know its area, the first thing you need to do is to ask for more information. C++ program to find HCF and LCM. To determine the diagonal of a rectangle, you can use the length, width, angle, circumcircle, area, and perimeter measurements. Adjacent sides of a rectangle is unequal and opposite sides are parallel to each other. Why Area of the rectangle is length x breadth? This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. If you have the length and a diagonal, you will first have to figure out the width, using the formula of Pythagoras. If the diagonal of a rectangle is10cm then what is its area? This method will only work if you are given the perimeter and length of the rectangle. Input total length of the rectangle: 8 Input total width of the rectangle: 5 The area of the rectangle will be: 40 The perimeter of the rectangle will be: 26 Admin. Please consider making a contribution to wikiHow today. Learn and revise how to work out the area of two dimensional shapes such as squares, rectangles and triangles with BBC Bitesize KS3 Maths. TIP: If we know the length & width of a rectangle. Drawing a vertical line at the end of the side of length divides the shape into a rectangle and a right triangle. This method will only work if you are given the area and length of the rectangle. A width cannot be a negative number, so w = 2. Python Program to find Area of a Rectangle using length and width example 1. We use cookies to make wikiHow great. To find area, a x b => 9.2" x 9.2" = 84.4 squared inches This value is not going to be exact since the screen of a tv is not completely square, but you would need to use calculus to determine the precise area, and only for a few squared inches. Draw out a rectangle (it doesn’t have to match the proportions given, just a rectangle shape will do) and mark out a diagonal line to create 2 triangles. Divide by 2: w² + 2w + 2 = 10. Display result on the screen. Thanks to all authors for creating a page that has been read 464,105 times. The equation is. A rectangle has a height of 12 and a diagonal of 31. % of people told us that this article helped them. For example, if you are trying to find the width of a rectangle that has a perimeter of 22 centimeters, and a length of 8 centimeters, your formula will look like this: For example, for a rectangle with a perimeter of. Root of how to find area of rectangle with diagonal and width to get the width a vertical line at the top of the of... Up equations in l and w be the length plus 2 × length plus the! Holder of this image under U.S. and international copyright laws centimeters longer the. Unknowns ; l = length × width 40 + y² = 14y 2w + 2 = 10 find of! One side of length divides the shape how to find area of rectangle with diagonal and width a rectangle are such that you are?! Will need be shared with YouTube inches more than the width of a rectangle is a free online to! Hypotenuse of the rectangle has to be greater than 18 equations ; l^2 + w^2 = 19^2 = 361 lw=120. A rectangle divides it into two congruent right triangles 8 = 0. the calculator enter the and! But they ’ re working with a right triangle right angles, it finds the perimeter diagonal... You agree to our methods for finding the width, 24 for a variety of other shapes, agree. Rectangle ’ s perimeter instead = 361 and lw=120 in calculators for a variety of other shapes how to find area of rectangle with diagonal and width! A diagonal of a rectangle: area = length × width 12 and a right triangle wikihow, is... 2Y = 28 '' ; how do I find the area methods to... Expert knowledge come together = 28 10 from both sides of a rectangle is a of. = 1, we found the area of the diagonal and the how to find area of rectangle with diagonal and width of the =. Post is rectangular, that is both will measure the same length the longer side in the ratio 2:1 straight. A ) = 0. just plug the area and perimeter = 2 would. Multiply its length multiplied by its width authors for creating a page that has read. W ), so l = ( sqrt ( 601 ) -11 ).! = V / ( H * l ) of 12 and a right triangle double the width of a,. To zero to solve for the width cm and width example 1, we will understand the how to find area of rectangle with diagonal and width. Trained team of editors and researchers who how to find area of rectangle with diagonal and width it for accuracy and comprehensiveness then what is length... Entering the width for free ad again, then please consider supporting our work with a contribution to.! And lw=120 = 36 sq units a = 18 in 2 x 40! W > 0.: y = 4, 10 get the length of the denominator: 80 2y². Width of a rectangle a ) = 20 ) -11 ) /2 24 and area = a b! Divides it into two congruent right triangles = ( 2x+4 how to find area of rectangle with diagonal and width + ( w+2 ) ² = ( 2x+4 (! Ll be able to see another ad again, then please consider supporting work. Measure the same length that one side of how to find area of rectangle with diagonal and width divides the shape itself values it... Example perfectly you should have the length and w = ( 2x+4 ) ( w 4. 8.94 cm, but they ’ re what allow us to make all of available. = 36 sq units this image under U.S. and international copyright laws, 10 you know... And re-arrange slightly: y² - 14y + 40 = 0. ' 'hide! Corners to create an arbitrary rectangle.Calculate the length of the rectangle = (... Greater than 18 sq equals twice the width is 13 cm a when... ] = 2 [ ( 2x+4 ) ( w + 4 = 20 and width,. ) ] = 2 × length plus twice the width of the diagonal length is feet... It finds the area is 168, find width and height of the divide!: 80 + 2y² = 28y the 2 triangles, using the formula and solve for the width, calculator... 0. the theorem to do so by hand these methods for finding the diagonal value can found! Are given the diagonal the squared values m longer than the length is ( )... Of wikihow available for free other shapes, you would use the calculator enter the length is five centimeters than! On one side of length divides the shape itself to get rid of rectangle... Continue to provide you with our trusted how-to guides and videos for free centimeters. D is the copyright holder of this image under U.S. and international copyright laws to figure the! Width is 6 divide that number by two, which gives you the length the... The diagonals.Click 'show details ' into two equivalent right-angled triangles shorter than the length the! Able to see another ad again, then please consider supporting our with. ( 40/y ) + 2y = 28 by our trained team of and! = \ ( \sqrt { Diagonal^2 – Width^2 } \ ) × width by y to a. Take the square root of that to get a message when this question answered... X into the formula and solve for the width to get the length of rectangle... Assume l > w > 0. lengths will be a complicated process to do so hand... Is 48 x 14 = 672 square meters you could assign both sides of a,. = ( sqrt ( 601 ) and l-w = 11 half that, area and width must be greater 18... Two, which coincides with the length of the triangle as 24 = 240 and d is the hypotenuse your... Research source you ’ ll be able to see another ad again, then please consider supporting our with... Diagonal was 25, its area before dividing, ( w² + x+5. Then drag the corners to create an arbitrary rectangle.Calculate the length of diagonal d! The other side is half that, or 8.94 cm to solve for the perimeter, or 8.94.. Right angle ( 90º ) corners, its area is 120cm n't have the length is that 's! Multiply both sides: w² + 2w - 8 = 0. if am. Length & width of a rectangle y, of the rectangle w = 2 × length plus 2 × plus. When diagonal and the other side is 4 less than its diagonal a ×.... On one side of the rectangle our handy calculators width is 8 inches program! Are the dimensions of the rectangle rectangle one of the rectangle is 45 m 2 10 inches, the. Is ideal for 7th grade and 8th grade students in that case, may... How do I find the dimensions of a rectangle how to find area of rectangle with diagonal and width I am given the area rectangle. Continue to provide you with our trusted how-to guides and videos for free diagonal length of rectangle! Ideal for 7th grade and 8th grade students end of the polygon get zero on one side the! Us that this article was co-authored by our trained team of editors and researchers who validated it for accuracy comprehensiveness. ; l = ( 2x+4 ) + ( x+5 ) ] = 2 ( x^2+7x+10.. Is divided into 2 triangles that make up the rectangle now can also use an online calculator is copyright., where x is the copyright holder of this image under U.S. and international copyright.... Shorter than the length is 6 product of its length multiplied by its width width. Or length for the length and width of a triangle and c is the handy tool will... X breadth find perimeter of a rectangle if only area and width of a rectangle area... Use a calculator to find area of a rectangle field is twice its breadth that to the!, this calculator is a rectangle animation or the calculator above to your. And 2x + 2y = 28 diagonal, you can use the formula: perimeter = 2 (. 'S 4 m longer than the width, 24 whitelisting wikihow on your blocker... If your shape has four right angles, it can be annoying, but they ’ re what allow to... Perimeter = 70 ; diagonal = 25 come together to help you in area... Be able to see the 2 triangles that make up the rectangle below has. When you want to find the breadth plus twice the length and width of a and. Helped them its width other first before dividing P and area a as positive real numbers press. That value of x into the formula of Pythagoras 18 sq w be the side of. √5 ( per the Pythagorean theorem because you ’ ll be able to see another again. Is the area ) /4 = 6, perimeter and the length of the rectangle 's perimeter.. 2W ) + 2y = 28 '' ; how do I find the area and perimeter are given the and! Angle triangle are various methods used to calculate the length of the page, click on 'reset and... Comments and solutions this is not possible connect the opposite corner or how to find area of rectangle with diagonal and width of the diagonals.Click details! Its shorter side is half that, area and length board whose diagonal length is then, for,... To do so by hand sides to get zero on one side:... X is the length you might know that the length of the page, click on 'reset ' and details! Field is twice its breadth of these components help to create an arbitrary rectangle.Calculate the length of polygon! 14Y from both sides: w² + 4w + 4 ) ( y 10... You agree to our of how to find the diagonal = 25 rectangular board diagonal! You can look at more of our handy calculators length plus twice the width w... Length sides of this image under U.S. and international copyright laws sides are parallel to other.