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Find the perimeter of the shaded region in figure 4, if ABCD is a square of side 14 cm and APB and CPD are semi-circles. use$\left( \pi=\frac{22}{7}\right)$.
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Given: Fig. 4, where ABCD is a square of side 14cm and APB and CPD are two semi-circles.

To do: To find the perimeter of the shaded region.

Solution: Here as given in the above question $ABCD$ is a square and $APB\ $and$\ CPD$ are two semi-circles.

$\because ABCD$ is a square.

$\because$  side of the square ABCD is 14 cm.

$\therefore AB=BC=CD=DA=14\ cm$ 

Here AB and CD are diameters off semi-circles APB and CPD.

$\therefore$ Radius of the semi-circles APB and CPD $=\frac{14}{2}$

$\therefore$Length of arc APB$=\frac{angle\ of\ the\ arc}{360^{0}} \times radius\ of\ the\ arc=\frac{180^{o}}{360^{o}} \times \frac{4}{2} =3.5\ cm$

Similarly length of arc $CPD=$length of arc$\ APB=3.5\ cm$

Perimeter of the shaded region$=AD+BC+$ length of arc APB $+$length of arc CPD

$=14+14+3.5+3.5$

$=35\ cm$

Thus the perimeter of the shaded region is 35 cm.

 

Updated on: 10-Oct-2022

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