waecmaths question:
In the diagram WXYZ is a rectangle with dimension 8 cm by 6 cm. P, Q, R and S are the midpoint s of the sides of the rectangle as shown.
Calculate the area of the part of the rectangle that is not shaded
Option A:
25 cm2
Option B:
24 cm2
Option C:
16 cm2
Option D:
12cm2
waecmaths solution:
$\begin{align} & WP=\tfrac{1}{2}(WX)=\tfrac{1}{2}(8cm)=4cm \\ & WS=\tfrac{1}{2}(WZ)=\tfrac{1}{2}(6cm)=3cm \\ & SP=\sqrt{{{4}^{2}}+{{3}^{2}}}cm=5cm \\ & SP=PQ=SR=PQ=5cm \\ & \text{Area of }SPQR=5cm\times 5cm=25c{{m}^{2}} \\ & \text{Area of }WXZY=8cm\times 6cm=48c{{m}^{2}} \\ & \text{Area of the unshaded portion}=48c{{m}^{2}}-25c{{m}^{2}}=23c{{m}^{2}} \\\end{align}$
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