Question

Find the area of the smaller sector.

Round to the nearest tenth.
50°
7.13 ft
Area = [?]ft²

Answer 1

Answer: 22.2 ft^2

Step-by-Step Solution:

Radius (r) = 7.13 ft
Angle (θ) = 50°

Area of a Sector = θ/360 * πr^2

Therefore,
= θ/360 * πr^2
= θ/360 * π * r * r
= 50/360 * 3.14 * 7.13 * 7.13
= 50/360 * 3.14 * 50.8369
= 5/36 * 159.63
= 798.15/36
= 22.17
=> 22.2

Area of the Sector = 22.2 ft^2

Answer 2

A ≈ 22.2 ft²

Explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

= πr² ×
`(50)/(360)`

= π × 7.13² ×
`(5)/(36)`

= 50.8369π ×
`(5)/(36)`

≈ 22.2 ft² ( to the nearest tenth )