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A memento is made as shown in the figure. What is the area of the region in the triangle excluding the part cut by the circle?

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138.20 c m^{2}

161.5 c m^{2}

133.567 c m^{2}

108.97 c m^{2}

answer is B.

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Detailed Solution

Given,

Required area

=

Area of triangle

-

Area of sector.
Area of a triangle is

\frac{1}{2} (base) (height)

.
Area of a sector is

\frac{x}{36 0^{°}} π r^{2}

\Rightarrow

Required area

= \frac{1}{2} \times 20 \times 20 - \frac{90^{°}}{360^{°}} \times \frac{22}{7} \times 7 \times 7

\Rightarrow

Required area

= \frac{400}{2} - \frac{77}{2} = \frac{323}{2}

\Rightarrow

Required area

= 161.5

{cm}^{2}

Hence, option 2 is correct.

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A memento is made as shown in the figure. What is the area of the region in the triangle excluding the part cut by the circle?

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