Calculate the area of a regular hexagon each of whose sides measures 6 cm. (Take √3 ≈ 1.732)
Answer and explanation
Correct answer: A. 93.53 cm²
- Step 1: A regular hexagon consists of 6 equilateral triangles of side s = 6 cm. Step 2. Area of one equilateral triangle: A_tri = (√3 / 4) s² = (√3 / 4)(36) = 9√3 cm². Step 3. Area of hexagon: 6 × 9√3 = 54√3 cm² ≈ 54 × 1.732 = 93.528 cm² ≈ 93.53 cm². Answer: 93.53 cm². Why not the others: 54.00 cm² omits the √3 multiplier; 108.00 cm² doubles 54; 81.25 cm² uses an incorrect height.
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