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JAMB Mathematics 2018 Paper

Question : 56

Total: 62

Calculate the area of an equilateral triangle of side 8cm

Solution:

Concept:

Area of a triangle using two sides and the included angle.

Explanation:

In an equilateral triangle, all sides are equal and each interior angle is

60^\circ

Use the formula:

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

, where

a = b = 8\,\text{cm}

and

\theta = 60^\circ

Substitute the values:

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

Since

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

, we get:

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

Simplify:

\text{Area} = 32 \times \frac{\sqrt{3}}{2} = 16\sqrt{3}\,\text{cm}^2

Answer:

16\sqrt{3}\,\text{cm}^2

(Option D).

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