SOLUTION: A circle is inscribed inside an equilateral triangle. If the circumference of the circle is 6 cm, then the area of the triangle, in cm^2 is:
A) 27 √3 π
B) 27 √3/π
C) 27
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-> SOLUTION: A circle is inscribed inside an equilateral triangle. If the circumference of the circle is 6 cm, then the area of the triangle, in cm^2 is:
A) 27 √3 π
B) 27 √3/π
C) 27
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Question 1167551: A circle is inscribed inside an equilateral triangle. If the circumference of the circle is 6 cm, then the area of the triangle, in cm^2 is:
A) 27 √3 π
B) 27 √3/π
C) 27 √3/π^2
D) 9 √3/π^2
E) 9 √3 π
Draw the three altitudes of the equilateral triangle, intersecting at the center of the circle. Those altitudes divide the equilateral triangle into six congruent 30-60-90 right triangles, in which the ratio of the side lengths is 1:sqrt(3):2.
(1) The circumference of the circle is 6; find the radius using .
(2) The radius of the circle is the short leg of one of the 30-60-90 right triangles. Use the radius from (1) and the ratio 1:sqrt(3):2 to find the long leg of each of the 30-60-90 triangles.
(3) The side length of the triangle is twice the length found in (2).
(4) The area of an equilateral triangle with side length s is .
If you do all those calculations correctly, you should finish with answer choice C.
