Find the area of the sector for the given radius and arc length s.

Question

find the area of the sector for the given radius and arc length a.

r=a , s=a

Answer 1

The area of a sector of a circle is given by:

A = (1 / 2) r² θ

where θ is measured in radians. Additionally, the arc length of a segment of a circle, s, is related to the radius of the circle by:

s = r θ -> θ = s / r

A = (1 / 2) r² (s / r) -> A = (1 / 2) r a

Finally, because s = a, and r = a:

A = (1 / 2) * a²

Answer 2

Area of a circle = 2rpi

2pi is the angle of a sector which is a circle

arc length = s=a = the angle times the radius, so the

angle = arc length divided by the radius = a/a = 1

Multiply the angle by the radius to get the area = 1 x a = a = area

the area = a