Question

1. The radius of the given circle is 7cm. Find the area of the shaded portion.​

Answer 1

$\Huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

• The Radius of the given circle is 7 cm

We have to find area of shaded region

$\rule{100}{2}$

In Δ AOB

∠AOB = 90°

Use formula of Area of right angle triangle

$\LARGE \implies {\boxed{\boxed{\green{\tt{(Area \: = \: \frac{1}{2} \: Base \: times \: height }}}}}$

Where,

Base is 7 cm

Height is 7 cm

(Putting Values)

→ Area = ½ × (7)(7)

→Area = ½ × 49

→Area = 24.5

$\Large{\boxed{\red{\sf{Area \: of \: \triangle \: = \: 24.5 \: cm^2}}}}$

$\rule{200}{2}$

Now in sector AOB

We have formula for area of sector :-

$\LARGE \implies{\boxed{\boxed{\green{\tt{\frac{\pi r^2 \: \theta}{360}}}}}}$

Now, take θ as 90°

→ Area of sector = π(7)² 90/360

→ Area of sector = 49π/4

→ Area of sector = 49 * 22/7 ÷ 4

→ Area of sector = 154/4

→ Area of sector = 38.5

$\Large{\boxed{\red{\sf{Area \: of \: Sector \: = \: 38.5 \: cm^2}}}}$

$\rule{200}{2}$

Area of Shaded Region => Area of Sector - Area of triangle

(Putting Values)

→ Area of shaded region = 38.5 - 24.5

→ Area of shaded region = 14

$\large \implies {\boxed{\red{\sf{Area \: of \: Shaded \: Region \: = \: 14 \: cm^2}}}}$

# See Figure for attachment

Answer 2

Answer:

14 cm²

Step-by-step explanation:

Area of sector =

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

$radius = 7 cm \\ \theta = 90 \\ \frac{22}{7} \times 7 \times 7 \times \frac{ 90}{360} \\ \\ 22 \times 7 \times \frac{1}{4} = 38.5 {cm}^{2}$

Now area of Right angled triangle =

$\frac{1}{2 } \times b \times h \\ \\ \frac{1}{2} \times 7 \times 7 = 24.5 {cm}^{2}$

Area of shaded region = Area of sector - Area of triangle

38.5 - 24.5 = 14 cm²