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Consider the above figure. What is the area in the given rectangle excluding the $6$ identical semicircles?

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144 c m^{2}

126 c m^{2}

195 c m^{2}

243 c m^{2}

answer is B.

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Detailed Solution

Given,

42 cm contains diameters of 3 semicircles.
Let r be the radius of a semicircle.
So, 3(2r) = 42.

\Rightarrow

r = 7 cm
Required area

=

Area of rectangle

- 6

\times

area of

1

semi-circle.
Area of a rectangle is (length)×(breadth).
Area of a semicircle is

\frac{π}{2} r^{2}

\Rightarrow

Required area

=

42 \times 14 - 6 \times \frac{1}{2} \times \frac{22}{7} \times 7 \times 7

\Rightarrow

Required area

= 588 - 462

\Rightarrow

Required area

= 126 {cm}^{2}

Hence, option 2 is correct.

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