WAEC Mathematics 2018 Paper

Concept:The shaded quadrilateral is formed by joining the midpoints of the sides of a rectangle. Its side lengths are equal because each side is the hypotenuse of the same sized right triangle.Explanation:The rectangle has length $8$ cm and breadth $6$ cm. The shaded quadrilateral connects the midpoints $P$, $Q$, $R$, and $S$. Along the horizontal direction, each side spans half the length: $\frac{8}{2} = 4$ cm. Along the vertical direction, each side spans half the breadth: $\frac{6}{2} = 3$ cm. Each side of the shaded quadrilateral is the hypotenuse of a right triangle with legs $4$ cm and $3$ cm.Using Pythagoras' theorem, $$\text{Side length} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ cm}$$All four sides of the shaded quadrilateral are equal to $5$ cm. Therefore, the shaded region is a rhombus.Answer:D. Rhombus