waecmaths question:
In the diagram O is the centre of circle and PQ is a diameter. Triangle of RSQ is an equilateral triangle of side 4cm. Find the area of the shaded region
Option A:
43.36cm2
Option B:
32.07cm2
Option C:
18.21cm2
Option D:
6.93cm2
waecmaths solution:
$\begin{align} & Area\text{ }of\text{ }\vartriangle ORS=\tfrac{1}{2}{{r}^{2}}\sin \theta =\tfrac{1}{2}{{(4)}^{2}}\sin {{60}^{\circ }}=8\times 0.8660=6.928c{{m}^{2}} \\ & Area\text{ }of\text{ }the\text{ }semi\text{ }circle=\frac{1}{2}(\pi {{r}^{2}})=\frac{1}{2}\times \frac{22}{7}\times {{4}^{2}}=25.14c{{m}^{2}} \\ & Area\text{ }of\text{ }the\text{ }shaded\text{ }portion=25.14c{{m}^{2}}-6.928c{{m}^{2}}=18.21c{{m}^{2}} \\\end{align}$
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