Geometry and TrigonometryVery hardArea of a regular polygon (hexagon)
Geometry and Trigonometry practice question
A regular hexagon has a side length of 4. What is its area? (A regular hexagon of side s has area (3√3/2)s².)
- A. 24√3Correct
- B. 12√3
- C. 48√3
- D. 96√3
Answer: A. 24√3
Area = (3√3/2)s² = (3√3/2)(4²) = (3√3/2)(16) = 24√3. A regular hexagon is six equilateral triangles of side 4; each has area (√3/4)(16) = 4√3, and 6 × 4√3 = 24√3. Choice B (12√3) counts only three of those triangles.
Why the other answers are wrong
- B. 12√3
- 12√3 is exactly half the area — a hexagon is six equilateral triangles of area 4√3 each, and you counted only three (or dropped the factor 3 in 3√3/2).
- C. 48√3
- 48√3 is what you get from 3√3 · 16 — you used the formula without dividing by 2.
- D. 96√3
- 96√3 comes from using 4³ = 64 instead of 4² = 16; the formula squares the side length.
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