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Find the area of the shaded region in fig., if PQ = 24 cm, PR

Question

Find the area of the shaded region in fig., if $PQ = 24 c m, PR = 7 c m$ and $O$ is the centre of the circle.

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Elijah Discussed

Find the area of the shaded region in fig., if

PQ = 24 c m, PR = 7 c m

and

O

is the centre of the circle.

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Area of shaded region

=

Area of semicircle

-

Area of

△

PQR

In right-angle triangle

PQR,

...(Triangle in a semicircle)

By pythagorous theorem,

= 2 4^{2} + 7^{2}

= 25 c m

∴

Area of semicircle

= \frac{π \times r ^{2}}{2}

= \frac{\frac{22}{7} \times 12.5 \times 12.5}{2}

= 245.54 c m^{2}

Area of

△

PQR

= \frac{1}{2} \times 24 \times 7

= 84 c m^{2}

∴

Area of shaded region

=

245.54 - 84

= 161.54 c m^{2}

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Question Text	Find the area of the shaded region in fig., if $PQ = 24 c m, PR = 7 c m$ and $O$ is the centre of the circle.
Answer Type	Text solution:1
Upvotes	150