OACB is a quadrant of a circle with centre O and radius 7 cm. If OD = 4 cm, then find the area of the shaded region.

18.5

c m^{2}

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20.5

c m^{2}

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22.5

c m^{2}

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24.5

c m^{2}

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Solution

The correct option is D 24.5 $c m^{2}$
For the quadrant $θ = 90^{\circ}$
Area of the quadrant $= \frac{θ}{360^{\circ}} \times π (r)^{2}$

Area of quadrant OACB = $\frac{90^{\circ}}{360^{\circ}} \times \frac{22}{7} \times (7)^{2} = \frac{77}{2}$

Area of shaded region = Area of quadrant OACB - Area of $△$ OAD

$= \frac{77}{2} - \frac{1}{2} \times 7 \times 4$

$= 24.5 c m^{2}$

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