If the side of a regular hexagon is 6 cm, what is its area?

Question

Examoogle · Accepted Answer

The correct answer is Option A: 54\sqrt{3} 	ext{ cm}^2. Since a regular hexagon consists of 6 equilateral triangles, memorize the area of one triangle as $\frac{\sqrt{3}}{4} a^2$ and multiply by 6 to get $\frac{3\sqrt{3}}{2} a^2$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Since a regular hexagon consists of 6 equilateral triangles, memorize the area of one triangle as $\frac{\sqrt{3}}{4} a^2$ and multiply by 6 to get $\frac{3\sqrt{3}}{2} a^2$.

Formula Used: $$Area = \frac{3\sqrt{3}}{2} 	imes a^2$$

Given: The side length (a) of a regular hexagon is 6 cm.

Steps: Identify the side length: The problem provides the side length $a = 6$ cm.. Apply the area formula for a regular hexagon: The area of a regular hexagon with side $a$ is given by the formula $	ext{Area} = \frac{3\sqrt{3}}{2} a^2$.. Calculate the final area: Substitute $a = 6$ into the formula: $6^2 = 36$. Then multiply: $\frac{3\sqrt{3}}{2} 	imes 36 = 3 	imes \sqrt{3} 	imes 18$.

Answer: A is correct because the area calculation $3 	imes 18 	imes \sqrt{3}$ results in $54\sqrt{3} 	ext{ cm}^2$.

Exam Tip: This concept is closely linked to 'Circles and Polygons' where the side of a regular hexagon inscribed in a circle is exactly equal to the radius of that circle ($a = R$).

Examoogle · Answer

Option B: 36\sqrt{3} 	ext{ cm}^2

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Option C: 18\sqrt{3} 	ext{ cm}^2

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Option D: 27\sqrt{3} 	ext{ cm}^2

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