Question

A sector of a circle with radius 21cm has an area of 280cm², find the perimeter of the sector.​

Answer 1

26.67 cm

Explanation:

Area of a sector

• A = πr² x θ/360°
• 280 = 22/7 x 21 x 21 x θ/360°
• 280 = 22 x 3 x 21 x θ/360°
• 40 = 22 x 9 x θ/360°
• 40 = 22 x θ/40°
• 1600 = 22 x θ
• θ = 1600/22 = 800/11 = 72.7°

Finding Perimeter (Arc Length)

• 2πr x θ/360°
• 2 x 22/7 x 21 x 800/11 x 1/360
• 2 x 22 x 3 x 800 x 1/11 x 1/360
• 132/11 x 800/360
• 12 x 20/9
• 12/9 x 20
• 4/3 x 20
• 80/3
• 26.67 cm