In the figure below, the triangle is equilateral and the radius of the circle is 1.
Determine the area of each colored region:
Area of Green region=
Area of Orange region =
Area of Yellow region =
Solution to the Problem:
First determine the areas of the triangle and the circle:
Note that the equilateral triangle can be divided into two 30-60-90 triangles.
In the diagram below, you can use the Pythagorean theorem to determine the sides of the special triangles (there are several 30 - 60 - 90 triangles).
Now, to find the area of the one of the Green regions, find the area of the 120 degree sector and then subtract the area of the 120 - 30 - 30 triangle:
Now, to find the area of the Yellow region, take the area of the large equilateral triangle and subtract the area of the circle and then add in the area of the Green region:
Now, to find the area of the Orange region, take the area of the circle and subtract the area of the Green region:
Correctly solved by:
| 1. James Alarie | Flint, Michigan |