Expert: Cynthia Watanabe - 10/20/2006

Question
How do you find the area of a circle contained within a triangle?

Answer
Thomas,

The radius of the circle is the same as the apothem of the triangle.

Draw the radius to the base and label it a for apothem.
Draw a segment from the center to the right vertex of the triangle.
You should "see" a right triangle now. Draw in the right angle.

To find the angle at the "top" of the RIGHT triangle which is the center of the circle, divide 360 degrees by 3(b/c of the outside triangle). Now divide that answer by 2 because the right triangle is only 1/2 of the central angle.

Now find the angle of the bottom right angle of the RIGHT triangle.

You should have a 30-60-90 degree triangle.

Use the 30 60 90 degree triangle to find the length of the apothem. The answer IS the length of the RADIUS.

Now, substitute the value for the radius into the formula for area of a circle. A= pi*r^2.

Keep asking questions! Take care, Cynthia