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What is the area of a regular hexagon with side-length 2?

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by Max@Math Revolution » Sun Nov 18, 2018 11:28 pm
[Math Revolution GMAT math practice question]

What is the area of a regular hexagon with side-length 2?

A. √2.
B. √3.
C. 2√2.
D. 2√3
E. 6√3
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by Byjus » Mon Nov 19, 2018 1:36 am
Hi,

Hexagon is a six-sided polygon.

Regular polygon means all sides and all angles are equal.

So regular hexagon is a 6-sided polygon with all sides and all angles are equal.

There are six equilaterals triangles with side length as "2".

Area of an equilateral triangle = (√3/4)*(side)^2
= (√3/4)*(2)^2 = (√3)

So, area of six equilaterals triangles = 6√3

So the answer is E.

Hope this helps.

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by Max@Math Revolution » Wed Nov 21, 2018 2:26 am
=>

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The area of an equilateral triangle with side-length a is (√3/4)a^2. So, the area of an equilateral triangle with side-length 2 is (√3/4)2^2 = (√3/4)4 = √3. Thus, the area of a regular hexagon with side-length 2 is 6√3.

Therefore, the answer is E.
Answer: E
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