Given:
θ = 60°
Radius = 8 in
To find:
The area of the shaded segment.
Solution:
Vertically opposite angles are congruent.
Angle for the shaded segment = 60°
Area of the sector:
[tex]$A=\pi r^2\times \frac{\theta}{360^\circ}[/tex]
[tex]$A=3.14 \times 8^2\times \frac{60^\circ}{360^\circ}[/tex]
A = 33.5 in²
Area of the sector = 33.5 in²
Area of triangle:
[tex]$A=\frac{1}{2} bh[/tex]
[tex]$A=\frac{1}{2} \times 8\times 8[/tex]
A = 32 in²
Area of the triangle = 32 in²
Area of segment = Area of sector - Area of triangle
= 33.5 in² - 32 in²
= 1.5 in²
The area of the shaded segment is 1.5 square inches.
