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JAMB Mathematics 2023 Paper

Question : 66

Total: 80

Calculate the area of the composite figure above.

Solution:

Concept:

The total area of a composite figure is found by adding the areas of the simple shapes that make it up.

Explanation:

The figure is made up of a semicircle, a rectangle, and a triangle.

The semicircle has diameter

42 \, \text{m}

, so its radius is

r = \frac{42}{2} = 21 \, \text{m}

Area of semicircle

= \frac{1}{2}\pi r^2 = \frac{1}{2} \times \frac{22}{7} \times 21^2 = 693 \, \text{m}^2

Area of rectangle

= \text{length} \times \text{breadth} = 42 \times 60 = 2520 \, \text{m}^2

Area of triangle

= \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 36 \times 42 = 756 \, \text{m}^2

Total area

= 693 + 2520 + 756 = 3969 \, \text{m}^2

Answer:

3969 \, \text{m}^2

(Option B).

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