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

Question

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?

Answer 1

Best Answer - Chosen by Asker

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

Asker's Rating:

Asker's Comment:

Thanks!

Answer 2

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.