How To Find Area Of Rectangle With Diagonal And Width

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When you're working with rectangles, you can find out a lot of information about them just by knowing a few key points of data. If you've been given the length of the diagonal and at least ane side, you tin can calculate the area of the whole shape with just a few equations. Always use a calculator to check your math, and don't forget to add your units onto the respond!

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Mark the diagonal on the rectangle. If you have a visual of your rectangle, it volition be a lot easier to figure out the expanse given a diagonal. Describe out a rectangle (information technology doesn't have to friction match the proportions given, just a rectangle shape will practise) and marker out a diagonal line to create 2 triangles.^[1]
- Y'all'll be able to see the 2 triangles that make up the rectangle now.
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4

Solve the equation to detect the missing side. Break downwards every number to its simplest form one step at a time to solve for the missing expression. When you're done, y'all can assign the answer to the missing side on your rectangle.^[4]
5

Plug the new number into $A=fifty\times w$ . To find the surface area of your entire rectangle, yous need to solve for Area = length 10 width, or A = 50 x w. At present that you've used the Pythagorean Theorem to find the 2nd side length, you can solve for the area. Don't forget your units!^[v]

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1
Marking the diagonal and side length on your rectangle. If you have a visual in front of you lot, information technology will be much easier to see how you lot're solving your equation. Depict a unproblematic rectangle with a ruler and create a diagonal line across it to make ii triangles.^[six]
- It's not mandatory to draw your triangle, but information technology tin can help you lot, especially if you're just starting out.
2
Enter the length and diagonal into $A=50\times {\sqrt {d^{2}-l^{2}}}$ . Merely plug the length and the diagonal into the formula to a higher place. Call up, the diagonal is always longer than the length of the rectangle. ^[7]
- For instance, if the length is 8 inches and the diagonal is 10 inches, the formula would be $A=8\times {\sqrt {10^{ii}-8^{2}}}$ .
3

Solve the equation to find the expanse. All you have to do now is break down the equation (using PEMDAS) in society to simplify information technology and get the surface area of the rectangle. For example:^[8]

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Question

If the diagonal of a rectangle is10cm then what is its area?

You lot don't accept plenty information to solve.
Question

A rectangle with diagonal of 20 cm has sides in the ratio 2:1. How do I detect the surface area of rectangle?

Such a rectangle would have its sides and diagonal in the ratio of two:1:√5 (per the Pythagorean theorem). The ratio of √5 to the diagonal (xx) is equal to the ratio of 2 to the longer side (or the ratio of one to the shorter side). Thus √5 : 20 = ii : x, where x is the longer side. Expressed every bit fractions, that's √5 / xx = 2 / x. Cross-multiplying: (√five)(x) = (20)(2). Dividing past √5: x = xl / √five = 40 / 2.236 = 17.nine cm. The shorter side is half that, or 8.94 cm.
Question

If the side = 48 meters and the diagonal = 50 meters, how practise I notice the area of the rectangle?

Let s exist the shorter side. Then (by the Pythagorean Theorem) south² + 48² = 50². And so s² + 2304 = 2500. Then southward² = 196, and southward = 14 m. The area is 48 10 14 = 672 square meters.
Question

The length of a rectangle is 2 inches more than the width. If the diagonal is the foursquare root of 20 inches, how do I find the area of the rectangle?

Let the width be due west. And so the length is (w+two). By the Pythagorean theorem, (westward²) + (w+ii)² = (√20)². And then w² + (w² + 4w + 4) = 2w² + 4w + 4 = 20. Split by 2: due west² + 2w + two = ten. Decrease 10 from both sides: due west² + 2w - 8 = 0. Then (w + 4)(w - ii) = 0. So w equals either -4 or +2. A width cannot be a negative number, so w = 2. The width is ii inches, the length is ii+2 or 4 inches, and the area of the rectangle is 2x4 or 8 square inches.
Question

If the diagonal length of a rectangle is 19cm and the area is 120cm. How do I discover the length and width?

Start by defining unknowns; 50 = length and w = width. Nosotros're given two equations; l^2 + due west^2 = 19^2 = 361 and lw=120. You lot can solve past substitution from hither -- you'll go a quartic, just it's really a quadratic in l^2 (or w^2 if yous substitute the other mode) and then y'all can yet solve it. But information technology goes a bit nicer if we don't pause symmetry but all the same and calculate (l+w)^2 = 50^2 + w^ii + 2lw = 361 + 240 = 601, and (l-w)^2 = l^two + w^2 -2lw = 361 - 240 = 121. So l+w = sqrt(601) and l-west = eleven. (Here, I presume l > w > 0.) And then l = (sqrt(601) + 11)/2 and w = (sqrt(601)-xi)/two.

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You lot can also use an online computer, like Omni Calculator, to bank check your work.
To discover the surface area of a rectangle, you need to know the diagonal and at to the lowest degree i side length.
If all you know is the length of the diagonal, you can calculate the area of a square, but not a rectangle.

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