Bunuel wrote:

If polygon ABCDE above has perimeter 26 and equilateral triangle BCD has perimeter 18, what is the area of the rectangular region ABDE?

(A) 6

(B) 12

(C) 24

(D) 32

(E) 48

Attachment:

2017-10-04_1125_003.png

Since equilateral triangle BCD has a perimeter of 18, each side is 6, which means that BC = CD = BD = 6. Furthermore, AE = 6 since AE = BD. If we let BA = DE = n, we can create the following equation to determine n:

BC + CD + DE + AE + AB = 26

6 + 6 + n + 6 + n = 26

2n = 8

n = 4

Thus, the area of rectangular region ABDE is 4 x 6 = 24.

Answer: C

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