Question

50 POINTS!!!

Find the area of the segment of circle C shown in the diagram above.

Answer 1

• B.the area =9.76u^2
• the area of the sector =1/2 x r^2 x (the angle in radian -sin(the same angle in degrees)

Answer 2

B. 9.76 u²

Explanation:

First calculate the area of the 60° wedge of the circle by calculating the area of the full circle and multiplying it by a fraction of 60°/360°:

`A_(ABC)=(60)/(360)*\pi *r^(2)\\A_(ABC)=(60)/(360)*\pi *(6√(3))^(2)\\A_(ABC)=56.54`

Now calculate the the area of the white triangle in the wedge, by using a base length of
`3√(2)`, and height:

`h=\sqrt{(6√(3))^(2)-(3√(3))^(2)} \\h=9`

`A_(TRI)=(1)/(2)*9*6√(3) \\A_(TRI)=27√(3) \\A_(TRI)=46.78`

Find the area of the red segment:

`A_(ABC) -A_(TRI)\\=56.54-46.78\\=9.76`