Question

AREA ADDITION AND SUBTRACTION ASSISTANCE?

Answer 1

The shaded area is a segment. The area of a segment is

`A_(segment)=A_(sector)-A_(triangle)`.

You know radius that is the side of isosceles triangle and measure of angle between two equal triangle sides, then

`A_(triangle) =(1)/(2) a\cdot a \sin \alpha=(1)/(2) 18.6\cdot 18.6 \cdot \sin 123^(\circ)=172.98\cdot \sin 123^(\circ)=145.07` sq. m..

The area of sector is
`A_(sector)=(r^2\cdot \alpha)/(2)= ((18.6)^2\cdot 0.68\pi)/(2)=117.63\pi=369.53` sq. m..

Then
`A_(segment)=369.53-145.07=224.46` sq. m.

Answer:
`A_(segment)=224.46` sq. m.