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# What is the formula of the area of a rectangle, using the perimeter and the diagonal?

I know that the area of a rectangle is height * width;
the perimeter: 2*width + 2*height
and that the diagonal is square_root(height² + width²),
but is there a formula to calculate the area with only the perimeter and diagonal given?
Member since:
February 15, 2007
Total points:
121,513 (Level 7)

Let rectangle length be L, width W, area A and perimeter P.

You correctly state that P = 2L + 2W and D^2 = L^2 + W^2 and A = LW.

D^2 = L^2 + W^2 = (L + W)^2 - 2LW = (P/2)^2 - 2A

2A = (P/2)^2 - D^2 ----> A = (1/2)((P/2)^2 - D^2) = (P^2)/8 - (D^2)/2
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• Member since:
August 26, 2006
Total points:
195 (Level 1)
Simple!
when there is a diagonal in the rectangle is means it is divided into two
right angled triangles.
area of a rectangle= sum of the two right angled triangles.
if u dunno the sides, then u can do with half perimeter nd diagonal for the right angled triangle area.

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