# Find the area of the shaded region if PAST is square of side 14 cm and ALS and PLT are semicircles.

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Given:

PAST is square of side 14 cm and ALS and PLT are semicircles.

To do:

We have to find the area of the shaded region.

Solution:

Here, as given in the above question $PAST$ is a square and $ALS$ and $PLT$ are two semi-circles.

$\because PAST$ is a square.

$\because$ Side of the square PAST is 14 cm.

$\therefore PA=AS=ST=TP=14\ cm$.

Here, PT and AS are diameters of semi-circles PLT and ALS.

$\therefore$ Radius of the semi-circles PLT and ALS $=\frac{14}{2}\ cm=7\ cm$.

Therefore,

Area of square PAST$=(14)^2\ cm^2=196\ cm^2$.

Area of semicircle PLT$=\frac{22}{7}\times\frac{7^2}{2}\ cm^2=11\times7\ cm^2=77\ cm^2$.

Area of semicircle ALS$=\frac{22}{7}\times\frac{7^2}{2}\ cm^2=11\times7\ cm^2=77\ cm^2$.

Area of the shaded region$=$Area of the square PAST$-$(Sum of the areas of semicircle PLT and ALS)

$=196-(77+77)\ cm^2$

$=196-154\ cm^2$

$=42\ cm^2$

**The area of the shaded region is $42\ cm^2$.**

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