NDA 1 2025 Maths, question 38

Topic: Trigonometry

Passage · Q36 to Q38

The sides of a triangle $ABC$ are $AB = 3$ cm, $BC = 5$ cm and $CA = 7$ cm.

Q38

What is the area of the triangle?

(a) $15\sqrt{3}/4$ square cmCorrect answer
(b) $15\sqrt{3}/2$ square cm
(c) $15\sqrt{3}$ square cm
(d) $30\sqrt{3}$ square cm

Solution.

Answer: (a) $15\sqrt{3}/4$ square cm

Using the included angle $B = 120^{\circ}$ , the area is $\frac{1}{2}(AB)(BC)\sin B = \frac{1}{2} \cdot 3 \cdot 5 \cdot \frac{\sqrt{3}}{2} = \frac{15\sqrt{3}}{4}$ square cm.
Hence option (a) is correct.