Calculating Area of Sector in Shaded Part of Diagram

[garyadamson]

I am trying to work out the area of the shaded part of the diagram. I've figured that If I was to work out the area of the triangle (27cm) and take it away from the sector, I'd have the area of the shaded bit.

I'm guessing that I'd have to use trigonometory to find the area of the sector, I really have no idea how to do this, and would appreciate some help. Thankyou

 

[chroot]

You're on the right track.

You know the area of the entire circle; it's pi times the radius squared.

You also know what fraction of that area is included in the sector; it's x/360, where x is in degrees.

- Warren

 

[garyadamson]

Thanks for your help
But how would I work out the size of angle X. Would cos, sin or tan have to be used?

 

[chroot]

You know all three sides -- use the law of cosines to find the angles.

- Warren

 

[robphy]

Less elegantly, you can break the triangle into two congruent right-triangles... then apply trigonometry with a right-triangle.

 

[Petkovsky]

Are you sure that the area of the triangle is 27cm?