Single correct option
ABCDEF is a regular hexagon with side 6 cm. What is the area of triangle ACE?
- A. 27√3 cm²
- B. 54√3 cm²
- C. 18√3 cm²
- D. 36√3 cm²
Show answer and solution
Answer: (A) 27√3 cm²
In a regular hexagon of side a, the short diagonal AC = a√3 (triangle ABC has sides a, a with a 120° angle between them).
So ACE is equilateral with side 6√3, and its area = (√3/4) × (6√3)² = (√3/4) × 108 = 27√3 cm².
Check: the hexagon's area is (3√3/2) × 36 = 54√3, and triangle ACE is exactly half of it.
So ACE is equilateral with side 6√3, and its area = (√3/4) × (6√3)² = (√3/4) × 108 = 27√3 cm².
Check: the hexagon's area is (3√3/2) × 36 = 54√3, and triangle ACE is exactly half of it.
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