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

Question

asked Oct 20, 2019 123k views

1 Answer

Dwalter · Answer 1 · 2019-10-27T08:17:43+0000

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

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