What is the area of the triangle?
Consider the following for the three (03) items that follow : The sides of a triangle ABC are AB=3\text{ cm}, BC=5\text{ cm} and CA=7\text{ cm}.
- A. 15\sqrt{3}/4 square cm ✓
- B. 15\sqrt{3}/2 square cm
- C. 15\sqrt{3} square cm
- D. 30\sqrt{3} square cm
Correct Answer: A. 15\sqrt{3}/4 square cm
Explanation
The area of the triangle is \Delta = \frac{1}{2}ac\sin B. Substituting a=5, c=3, and B=120^{\circ}, we get \Delta = \frac{1}{2}(5)(3)\sin 120^{\circ} = \frac{15}{2}(\frac{\sqrt{3}}{2}) = \frac{15\sqrt{3}}{4} \text{ cm}^2.