Areas

Area of a segment

A segment of a circle is the region between a chord of a circle and its associated arc.

Area of a segment in a circle
The area of a segment in a circle is found by first calculating the area of the sector formed by the two radii and then subtracting the area of the triangle formed by the two radii and chord (or secant)

Area = $\frac{\pi\;\cdot\;r^2\;\cdot\;x}{360}\;-\;\frac{b\;\cdot\;h}{2}$

Find the shaded area.

Area = $\frac{\pi\;\cdot\;r^2\;\cdot\;x}{360}\;-\;\frac{b\;\cdot\;h}{2}$

r=4cm
x=90º
b=4cm
h=4cm

Area = $\frac{\pi\;\cdot\;4^2\;\cdot\;90}{360}\;-\;\frac{4\;\cdot\;4}{2}$ = 4 $\pi$ -8 m²