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Chapter 8: Q. 38 (page 541)

See the following figure. Find the area

of the shaded region enclosed in a semicircle of diameter 10 inches. The length of the chord PQ is 8 inches.

Short Answer

Expert verified

The area of the shaded part is15.27sq.units

Step by step solution

01

Given information

We are given a figure

02

Use Pythagoras theorem to find the length of QR

By Pythagoras theorem

PQ2+QR2=PR282+QR2=10264+QR2=100QR2=36QR=6

03

Find the area of Semicircle and triangle

Area of semicircle

Ks=蟺r22Ks=蟺(5)22Ks=39.27sq.units

Area of triangle

Kt=ab2Kt=8(6)2Kt=24sq.units

04

Find the area of shaded region

Area of shaded region is

Kr=Ks-KtKr=39.27-24Kr=15.27sq.units

05

Conclusion

The area of shaded region is 15.27sq.units

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