Let's say the width of the shed is W and the length is L. Then we know that
2W + 2L = 40, or W + L = 20 and
W2 + L2 = 152 = 225.
If we square both sides of the first equation, we get
(W+L)2 = 400
W2 + L2 + 2WL = 400.
Since we know that W2 + L2 = 225, we can simplify the equation to
225 + 2WL = 400
2WL = 175
WL = 87.5
The quantity WL is the area of the shed, since the area of a rectangle is width times length. So the correct answer is D.