Question

If the radius of circle A is 6 units, calculate the area of the shaded region...

Answer 1

The formula of an area of a triangle:

`A_(\triangle)=(base\cdot height)/(2)`

We have:

`\triangle_(FDE):\ base=height=1\\\triangle_(GDH):\ base=height=9`

substitute:

`A_{\triangle_(FDE)}=(1\cdot1)/(2)=0.5\\\\A_{\triangle_(GDH)}=(9\cdot9)/(2)=40.5`

The formula of an area of a circle:

`A_O=\pi r^2`

We have
`r=6`

Substitute:

`A_O=\pi\cdot6^2=36\pi\approx36\cdot3.14=113.04`

The area of the shaded region

`A=A_O-(A_{\triangle_(FDE)}+A_{\triangle_(GDH)})\\\\A=113.04-(0.5+40.5)=113.04-41=72.04\ u^2`