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:[tex] \sqrt{3} [/tex]:2. In our case the hypotenuse is 6, so the ratio is 3:3[tex] \sqrt{3} [/tex]:6.
The area of each triangle is:
A = (3*3[tex] \sqrt{3} [/tex])/2
So for all 6 it will be
Total area = 27[tex] \sqrt{3} [/tex] ft²= 46.77 ft²
