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The figure shown is a regular hexagon with center h.

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The figure shown is a regular hexagon with center h.

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

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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