theCodeToGMAT wrote:If ABCD is a square with area 625, and CEFD is a rhombus with area 500, then the area of the shaded region is
Note: Figure not drawn to scale
(A)125
(B)175
(C)200
(D)250
(E)275
Answer [spoiler]{E}[/spoiler]
Square ABCD:
Since area = s² = 625, AD=25.
Rhombus AHGD:
Since area = bh = (AD)(EH) = 500, we get:
25(EH) = 500
EH = 500/25 = 20.
∆AHE:
Since AD=25 in rhombus AHGD, AH=25.
Since AH=25 and EH=20, ∆AHE is a 3:4:5 triangle in which each side is multiplied by 5:
3:4:5 = 15:20:25.
Thus, AE = 15.
Area of ∆AHE = (1/2)bh = (1/2)(AE)(EH) = (1/2)(15)(20) = 150.
Rectangle EHFD:
Since ED = 25-15 = 10, area = bh = (ED)(EH) = 10*20 = 200.
Shaded region = Square ABCD - ∆AHE - Rectangle EHFD = 625-150-200 = 275.
The correct answer is
E.
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