Question 50

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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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