Find the area of a segment formed by a chord 8" long in a circle with a radius of 8"?

Solution:

If the length of the chord is 8’’, then α = 60° = π/3(since it is an equilateral triangle)

We know that

Area of the segment = 1/2 r² (α - sin α)

Where r is the radius

Substituting the values

Area of the segment = 1/2 (8)² (π/3 - sin π/3)

Converting into radians and getting the sin value, we get

Area of the segment = 1/2 × 64 × (1.046 - 0.866)

Area of the segment = 5.76 in²

Therefore, the area of the segment is 5.76 in².

Find the area of a segment formed by a chord 8" long in a circle with radius of 8"?

Summary:

The area of a segment formed by a chord 8" long in a circle with radius of 8" is 5.76 in².