Friday, October 5, 2007

A-Math Circular Measure

5 marks, showing qn.


Lustrous Realm said...

You can form 2 equilateral triangles within the shaded region itself and the length of each side is 2r.

Next is to find the total area of these 2 triangles. You can use the equation half x base x height. The base is 2r and the height can be found with pythagoras theorem.

Since we know that there are 2 equilateral triangles, we will know that the angle is 120 degrees. Thus, find the area of the sector now using the formula half x radius squared x theta. The theta is 120 x pi divide 180.

Use this value to minus off the total area of the 2 equilateral triangles found earlier. Name this value x.

The answer can then be proven by the following expression:

2x + Total Area of the 2 equilateral triangles.

Good luck to you in your Prelims XD