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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