A regular hexagon has perimeter 36 cm. What is its total area?
Answer and explanation
Correct answer: B. 54*sqrt(3) cm^2
- Step 1: Side length s = 36 / 6 = 6 cm.
- Step 2: A regular hexagon is composed of 6 equilateral triangles of side s = 6.
- Step 3: Area of one equilateral triangle = (sqrt(3)/4) s^2 = (sqrt(3)/4) 36 = 9*sqrt(3) cm^2.
- Step 4: Total area = 6 9sqrt(3) = 54*sqrt(3) cm^2.
Answer
54*sqrt(3) cm^2.
Why not the others: 36sqrt(3) computes area for s = 4; 72sqrt(3) uses 8 triangles; 108 cm^2 estimates sqrt(3) as 2.
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