Single correct option
ABCDEF is a regular hexagon of side 6 cm. What is the area (in cm²) of triangle ACE?
- A. 18√3
- B. 27√3
- C. 36√3
- D. 54√3
Show answer and solution
Answer: (B) 27√3
In a regular hexagon of side a, the 'short diagonal' AC = a√3 (angle ABC = 120°, so AC² = a² + a² − 2a²cos120° = 3a²).
Triangle ACE is equilateral with side 6√3.
Area = (√3/4)(6√3)² = (√3/4)(108) = 27√3.
Check: the hexagon's area is 54√3, and triangle ACE is exactly half of it (the three small triangles ABC, CDE, EFA make up the other half). 54√3 is the trap option.
Triangle ACE is equilateral with side 6√3.
Area = (√3/4)(6√3)² = (√3/4)(108) = 27√3.
Check: the hexagon's area is 54√3, and triangle ACE is exactly half of it (the three small triangles ABC, CDE, EFA make up the other half). 54√3 is the trap option.
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