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JAMB Mathematics 2024 Paper

Question : 15

Total: 50

\angle

PQR

Solution:

Concept:

Use the formula for the area of a triangle when two sides and the included angle are known:

\text{Area} = \frac{1}{2}ab\sin\theta

Explanation:

Given

|PQ| = |QR| = 8\text{ cm}

and

\angle QPR = 60^\circ

, the sides

PQ

and

QR

are equal, so the base angles are equal.

Thus

\angle QPR = \angle PRQ = 60^\circ

Therefore

\angle PQR = 60^\circ

, and the triangle is equilateral.

Each side is therefore

8\text{ cm}

Now take two adjacent sides as

8\text{ cm}

and

8\text{ cm}

, with the included angle

60^\circ

\text{Area} = \frac{1}{2} \times 8 \times 8 \times \sin 60^\circ

\text{Area} = \frac{1}{2} \times 64 \times \frac{\sqrt{3}}{2}

\text{Area} = \frac{64\sqrt{3}}{4} = 16\sqrt{3}\text{ cm}^2

Answer:

16\sqrt{3}\mathrm{cm}^2

(Option A).

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