How do you solve this?

enter image source here

1 Answer
Jun 16, 2018

I tried this but check my maths...

Explanation:

Consider the Diagram:
enter image source here

I would use Trigonometry to find the sides of triangle AOC:

rAC=tan(30)

AC=3tan(30)=5.2

and:

r=OCsin(30)

OC=3sin(30)=6

the area of the triangle AOC will be:

Area1=ACr2=7.8u.a.

we can multiply by 2 to get the area of the two tringles:

Area Triangles=2Area1=27.8=15.6u.a.

We can subtract from this area the area of the circular sector AOB to get the violet area:

Area Aector=12r2angle in radians=123223π=9.4u.a.

So the final area should be:

Area shaded=15.69.4=6.2u.a.