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22.2 ft²

Step-by-step explanation:

The area (A) of the sector is

A = area of circle × fraction of circle

   = πr² ×

   = π × 7.13² ×

   = π × 50.8369 ×

   = ≈ 22.2 ft² ( nearest tenth )

Area of smaller sector = 22.2 ft²

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where 'r' is the radius of circle

To find the area of circle

Here r = 7.13 ft

Area =  πr²

 =  3.14 * 7.13²

 = 159.63 ft²

To find the area of smaller sector

Here central angle of sector is 50°

Area of sector = (50/360) * area of circle

 = (50/360) * 159.63

 = 22.17 ≈ 22.2 ft²

20

step-by-step explanation: