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:

$A_{\triangle}=\dfrac{base\cdot height}{2}$

We have:

$\triangle_{FDE}:\ base=height=1\\\triangle_{GDH}:\ base=height=9$

substitute:

$A_{\triangle_{FDE}}=\dfrac{1\cdot1}{2}=0.5\\\\A_{\triangle_{GDH}}=\dfrac{9\cdot9}{2}=40.5$

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

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