Length of certain sector of circle of radius 5.6cm is17.2cm find the area of the sector?
Answers
The area of the sector is 16.60 cm^2
Step-by-step explanation:
Given data:
Radius of the circle, r = 5.6 cm
Perimeter of the sector = 17.2 cm
Let θ be the angle subtended by the sector at the centre of the circle.
θ / 360° x 2πr + 2r = 17.2
(θ / 360° x π + 1) 2r = 17.2
(θ / 360° x π + 1) 2 x 5.6 = 17.2
(θ / 360° x π + 1) 2 x 5.6 = 17.2
(θ / 360° x π + 1) x 11.2 = 17.2
(θ / 360° x π + 1) = 17.2/11.2
(θ / 360° x π + 1) = 1.53
θ / 360° x π = 1.53 - 1
θ / 360° x π 0.53
Area of the sector
= θ / 360° x πr^2
= 0.53 x (5.6)^2
= 0.53 x 31.36 = 16.60 cm^2
Thus the area of the sector is 16.60 cm^2
Also learn more
The perimeter of a rectangle is 96 ft. Find the dimensions of the rectangle if the ratio of the length to the width is 7 : 5. Which of the following would be the best equation to use to solve this problem?
https://brainly.com/question/7134956