Question

Find the perimeter and area of the shaded region in the below figure.
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Answer 1

Given:

Radius of circle = OA= 7 cm

Angle of sector =∠BOA = 60°

To find:

We are asked to find the Area of shaded region PBA

Solution:

Area of PBA = Area of ΔAOB - Area of sector AOP

(i) Area of ΔAOB

From the figure

Tan 60° = BA/AO

√3 = BA/7

BA = 7√3 cm

Now Area = $\frac{1}{2}(AO)(BA)$

                 = $\frac{1}{2}(7)(7\sqrt{3} )$

                 = $\frac{49\sqrt{3} }{2}$

Area of ΔAOB = 42.435 sq.cm

(ii) Area of sector = $\frac{\theta}{360}{\pi}r^{2}$

Here Θ = 60°   r = 7

Area = $\frac{60}{360}{\pi}7^{2}$

        = $\frac{49}{6}{\pi}$

Area = 25.656 sq.cm

Now Area of shaded region = 42.435 - 25.656 = 16.779 sq.cm

∴ The Area of shaded region = 16.779 cm²