Vincen wrote: ↑

Tue Aug 18, 2020 7:52 am

2018-07-23_1017.png

The hexagonal face of the block shown in the figure above has sides of equal length and angles of equal measure. If each lateral face is rectangular, what is the area, in square inches, of one lateral face?


(A) \(2\sqrt{10}\)

(B) \(12\)

(C) \(20\)

(D) \(12\sqrt3\)

(E) \(24\)


Answer: E

Source: GMAT Paper Tests

Solution:

Since the sides of the hexagon are equal in length and the angles of the hexagon are equal in measure, the hexagon is regular. In a regular hexagon, its longest diagonal is twice its side length. Since here that diagonal is 24 inches, a side of the hexagon is 12 inches. Since this is also the length of a rectangular lateral face of the hexagonal block and the width of a lateral face is 2 inches, the area of a lateral face is 12 x 2 = 24 sq. in.

Answer: E