Problem Solving

AAPL wrote:Magoosh



If ABCD is a square with area 625, and CEFD is a rhombus with area 500, then the area of the shaded region is

A. 125
B. 175
C. 200
D. 250
E. 275

OA E.

Let's the image.



We have to find out the area of CABF'EC.

Area of CABF'EC = Area of ABCD - Area of CEFD + Area of DF'F

Area of ABCD = 625 (given)
Area of CEFD = 500 (given)

To get the area of DF'F, we need the values of DF' and F'F.

Area of CEFD = CD * F'D = √625 *F'D = 25F'D = 500 => F'D = 500/25 = 20

Thus, F'F = √(25^2 - 20^2) = 15

Thus, area of DF'F = 1/2 * F'D * F'F = 1/2 * 20 * 15 = 150

Area of CABF'EC = Area of ABCD - Area of CEFD + Area of DF'F = 625 - 500 + 150 = 275

The correct answer: E

Hope this helps!

-Jay
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