In the given figure, AOB is a sector of angle 60° of a circle with centre O and radius 17 cm. If AP ⟂ AB

Question

In the given figure, AOB is a sector of angle 60° of a circle with centre O and radius 17 cm. If AP ⟂ OB and AP = 15 cm, find the area of the shaded region.

Answer 1

AOB is a sector of angle 60° of a circle with centre O and radius 17

If AP ⟂ OB and AP = 15 cm

Now we have to find the area of the shaded region.

 In ∆OPA, ∠O = 90°

By using Pythagoras theorem 

AO² = AP² + OP²

17² = 15² + OP² 

OP² = 289 − 225 

OP² = 64

OP = 8 cm

Area of shaded region = Area of sector AOBA − Area of ∆OPA

\(= \frac x{360} \times \pi r^2 - \frac 12 \times b \times h\)

\(= \frac{60}{360} \times \frac{22}7 \times 17 \times 17 - \frac 12 \times 8 \times 15\)

\(= \frac 16 \times \frac{22}7 \times 289 - 60\)

\(= 151.38 - 60\)

\(= 91.38\) cm²

Hence the area of the shaded region is 91.38 cm².

Answer 2

= 151.38 - 60 = 91.38 cm²