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

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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 ...show more
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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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  • karthik s answered 5 years ago
    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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