The figure shown is a regular hexagon with center h.

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon Mar 25, 2019 9:27 pm

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The figure shown is a regular hexagon with center h. the shaded area is a parallelogram that shares three vertices with the hexagon and its fourth vertex is the center of the hexagon. If the length of one side of the hexagon is 8 centimeters, what is the area of the unshaded region?

A) $16\sqrt{3}cm^2$
B) $96 cm^2$
C) $64\sqrt{3}cm^2$
D) $96\sqrt{3}cm^2$
E) $256cm^2$

OA C

Source: Princeton Review

Source: Beat The GMAT — Problem Solving | Mon Mar 25, 2019 9:27 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Mar 25, 2019 11:32 pm

BTGmoderatorDC wrote:

The figure shown is a regular hexagon with center h. the shaded area is a parallelogram that shares three vertices with the hexagon and its fourth vertex is the center of the hexagon. If the length of one side of the hexagon is 8 centimeters, what is the area of the unshaded region?

A) $16\sqrt{3}cm^2$
B) $96 cm^2$
C) $64\sqrt{3}cm^2$
D) $96\sqrt{3}cm^2$
E) $256cm^2$

OA C

Source: Princeton Review

Since it is given that the hexagon is a regular hexagon, the unshaded region can be divided into 4 equal equilateral triangles.

Area of an equilateral triangle = √3/4a^2; where a = side of the equilateral triangle

=> Area of the unshaded region = Area of 4 equilateral triangles = 4*√3/4a^2 = √3a^2 = √3*8^2 = 64√3 cm^2

The correct answer: C

Hope this helps!

-Jay
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