Question

The logo for a school is an equilateral triangle inscribed inside a circle. The seniors are painting the logo on an outside wall of the school. The radius of the circle will be 6 feet. Find the area of the triangle.

Answer 1

Try to do this on paper and follow my instructions:

Draw lines from the corner of the triangle towards the center of the circle. These will each have a length of 6'.

Now draw a line bisector from the center perpendicular to the sides of the triangle. Now you have 6 triangles of 30-60-90 degree angles.

Each 6 triangle has similar shape as half an equilateral triangle with side ratios of 1:
`√(3)`:2. In our case the hypotenuse is 6, so the ratio is 3:3
`√(3)`:6.

The area of each triangle is:

A = (3*3
`√(3)`)/2

So for all 6 it will be

Total area = 27
`√(3)` ft²= 46.77 ft²