GRE Big Book Test 10 Section 3 Q15

[user2626]

Why is the fraction of the shaded area 7/16?
Answer is C(Both quantities are equal)

[user2791]

let AC = CE = EF = FA = 4
now we know D and B are mid points of CE and AC respectively. i.e CD = DE = 2 = AB = BC

now area triangle BCD = (1/2) * CD * BC = 2
and area of square is 16

now to find the area of ABDEF we need to subtract the area of triangle BCD from the square ACEF and we get the area i.e. 14 and now to find the area of shaded region just divide ABDEF into half and we get the shaded area i.e 7

now the question is askingfraction of shaded region to square and we get 7/16

so option “C” is the answer