How do you solve this?

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Answer 1 · 2018-06-16T23:43:32

I tried this but check my maths...

Consider the Diagram:
enter image source here

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

#r/(AC)=tan(30^@)#

#AC=3/tan(30^@)=5.2#

and:

#r=OCsin(30^@)#

#OC=3/sin(30^@)=6#

the area of the triangle AOC will be:

#"Area1"=(AC*r)/2=7.8 "u.a."#

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

#"Area Triangles"=2*"Area1"=2*7.8=15.6"u.a."#

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

#"Area Aector"=1/2r^2*"angle in radians"=1/2*3^2*2/3pi=9.4"u.a."#

So the final area should be:

#"Area shaded"=15.6-9.4=6.2"u.a."#