Question

Find the Perimeter and Area of the Shaded region given in the figure.
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Answer 1

Answer:

16.774

Step-by-step explanation:

area of sector =

$\frac{theta}{360} \pi \: {r}^{2}$

60 /360 × 3.14 × 7×7

= 25.66 cm^2

in triangle AOB

tan 60 = AB/ AO

√3=AB/7

AB= 7√3 cm

Area of triangle AOB

= 1/2 * b*h

= 1/2 * 7 * 7√3

= 42.434 cm ^2

Area of shaded region

= 42.434- 25.66

= 16.774 cm^2

In triangle AOB

sin theta = AB/BO

Sin 60 = 7√3/BO

√3/2=7√3 ÷BO

BO= 14cm

length of arc PA

theta / 360 × 2 pi r

= 60 / 360 × 2 × 3 .14 × 7

=7.3cm

perimeter of shaded region

= AB+PB+AP

= 7√3+ (14-7) + 7.3

=26.424 cm