Single correct option
ABCDEF is a regular hexagon of side 6 cm. What is the area of triangle ACE?
- A. 18√3 cm²
- B. 27√3 cm²
- C. 36√3 cm²
- D. 54√3 cm²
Show answer and solution
Answer: (B) 27√3 cm²
In a regular hexagon of side a, the short diagonal AC = a√3 = 6√3 (triangle ABC has angle 120° at B: AC² = 36 + 36 + 36 = 108).
Triangle ACE is equilateral with side 6√3, so its area = (√3/4) × 108 = 27√3 cm².
Shortcut: triangle ACE is exactly half the hexagon. Hexagon area = (3√3/2) × 36 = 54√3, half of which is 27√3.
Triangle ACE is equilateral with side 6√3, so its area = (√3/4) × 108 = 27√3 cm².
Shortcut: triangle ACE is exactly half the hexagon. Hexagon area = (3√3/2) × 36 = 54√3, half of which is 27√3.
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