Single correct option
ABCDEF is a regular hexagon with side 4 cm. What is the area of triangle ACE?
- A. 16√3 cm²
- B. 24√3 cm²
- C. 8√3 cm²
- D. 12√3 cm²
Show answer and solution
Answer: (D) 12√3 cm²
In a regular hexagon each interior angle is 120°. In triangle ABC, AB = BC = 4 and ∠B = 120°, so
AC² = 16 + 16 − 2 · 16 · cos 120° = 48 → AC = 4√3.
Triangle ACE is equilateral with side 4√3, so its area = (√3/4) × 48 = 12√3 cm².
Check via ratio: Hexagon area = (3√3/2) × 16 = 24√3; triangle ACE is exactly half of the hexagon.
AC² = 16 + 16 − 2 · 16 · cos 120° = 48 → AC = 4√3.
Triangle ACE is equilateral with side 4√3, so its area = (√3/4) × 48 = 12√3 cm².
Check via ratio: Hexagon area = (3√3/2) × 16 = 24√3; triangle ACE is exactly half of the hexagon.
Saved on this device. Sign in or create a free account to keep it on every device.