Test Index

UPSC NDA I 2025 Mathematics Paper

Question Numbers: 36-38

Consider the following for the three (03) items that follow: The sides of a triangle ABC are A

B=3

cm, B

C=5

cm and C

A=7

cm.

Question : 38 of 120

Marks: +1, -0

What is the area of the triangle?

Solution:

Concept:

Area of a triangle when two sides and the included angle are known is given by

\frac{1}{2} \times \text{product of sides} \times \sin(\text{included angle})

Explanation:

Given sides

a = 5

cm and

c = 3

cm with included angle

B = 120^\circ

Apply formula:

\text{Area} = \frac{1}{2} \times 5 \times 3 \times \sin 120^\circ

\sin 120^\circ = \sin(60^\circ) = \frac{\sqrt{3}}{2}

\text{Area} = \frac{1}{2} \times 15 \times \frac{\sqrt{3}}{2} = \frac{15\sqrt{3}}{4}

square cm.

Answer:

The area is

\frac{15\sqrt{3}}{4}

square cm. Hence, the correct answer is Option 1.

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