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ABCD is a flower bed. If $OA = 21 cm$ and $OC = 14 m$ . What is the area of the bed?

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161.4 m^{2}

192.5 m^{2}

212.6 m^{2}

257.2.5 m^{2}

answer is B.

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Detailed Solution

Given,

We have,

OA = R = 21 m

and

OC = r = 14 m

.
Area of a quadrant =

\frac{1}{4} π R^{2}

∴

Area of the flower bed =Area of a quadrant of a circle of radius R - Area of a quadrant of a circle of radius r.

\Rightarrow

Area of the flower bed

= \frac{1}{4} π R^{2} - \frac{1}{4} π r^{2}

\Rightarrow

Area of the flower bed

= \frac{π}{4} (R^{2} - r^{2})

\Rightarrow

Area of the flower bed

= \frac{1}{4} \times \frac{22}{7} (21^{2} - 14^{2}) c m^{2}

[∴ R = 12 m

and

r = 14 m]

\Rightarrow

Area of the flower bed

= (\frac{1}{4} \times \frac{22}{7} \times (21 + 14) (21 - 14)) m^{2}

\Rightarrow

Area of the flower bed

= (\frac{1}{4} \times \frac{22}{7} \times 35 \times 7) m^{2} = 192.5 m^{2}

Hence, option 2 is correct.

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ABCD is a flower bed. If OA=21cm and OC=14m. What is the area of the bed?

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ABCD is a flower bed. If $OA = 21 cm$ and $OC = 14 m$ . What is the area of the bed?