Question

11(a). Two regular polygons P and Q are such that the number of sides of P is twice the number of sides of Q. The difference between the exterior angle of Q and P is 45°. Find the number of sides of P.
11(b). The area of a semi-circle is 32π cm². Find, in terms of π, the circumference of the semi-circle.

Accepted Answer

(a) Let sides of Q=n_q, sides of P=n_p=2n_q. Exterior angle of P=360/n_p, exterior angle of Q=360/n_q. Difference: 360/n_q - 360/n_p=45° → 360/n_q-360/2n_q=45 → 180/n_q=45 → n_q=4. So n_p=2×4=8 sides.

(b) Area of semicircle=(1/2)πr²=32π → r²=64 → r=8cm. Diameter=2r=16cm. Circumference of semicircle=D+length of arc of semicircle=16+πr=16+8π, or (16+8π) cm.

WAEC Mathematics 2023 Theory — Question 11

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