Question

Hey Everyone! Please can you solve the attached problem? Provide step by step work please...

Answer 1

AnsWer :

56 cm².

Given :

• Length of the arc is 22 cm.
• Radius of the Circle is 14 cm.

Concepts Required :

• Area of sector,

$\longrightarrow \tt \frac{ \theta .\pi {r}^{2} }{360 \degree}$

• Area of arc.

$\tt \longrightarrow\frac{ \theta.2 \pi r}{360 \degree}$

Solution :

Area of arc,

$\tt \implies\frac{ \theta.2 \pi r}{360 \degree} = 22$

$\tt \implies\frac{ \theta.2 \times 22 \times 14 }{360 \degree \times 7} = 22.$

$\tt \implies \theta = 90 \degree.$

Area of Triangle,

$\longrightarrow \frac{1}{2} \times (base)(height)$

$= \tt \frac{1}{2} \times 14 \times 14. \\ \tt = 7 \times 14. \\ = \tt98 \: c {m}^{2}.$

Area of sector,

$\longrightarrow \tt \frac{ \theta .\pi {r}^{2} }{360 \degree}$

$= \tt \frac{ \theta .\pi {r}^{2} }{360 \degree} . \\ \tt = \frac{90.22 \times 14 \times 14}{360 \times 7}$

$= \tt154.$

Now,

Area of segment = area of sector - area of triangle.

$= \tt154 - 98. \\ = \tt 56 \: c {m}^{2} .$

Therefore, the required answer is 56 cm².