In a triangle ABC, \angle ABC=60^\circ and AD is the altitude. If AB = 6 cm and BC=8 cm then what is the area of the triangle?
- A. 12 square cm
- B. 12\sqrt{3} square cm ✓
- C. 24 square cm
- D. 24\sqrt{3} square cm
Correct Answer: B. 12\sqrt{3} square cm
Explanation
The area of a triangle can be found using the formula \frac{1}{2}ab \sin C. Applying this gives \text{Area} = \frac{1}{2} \times AB \times BC \times \sin(\angle ABC) = \frac{1}{2} \times 6 \times 8 \times \sin 60^\circ = 24 \times \frac{\sqrt{3}}{2} = 12\sqrt{3} cm^2.
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