SOLUTION: In the equilateral triangle illustrated below, O is the circumcentre of the triangle, and OA = 2 sqrt3 cm. Find the area of the triangle, in cm2. Diagram: https://imgur.com/a/OI

Question 1149199: In the equilateral triangle illustrated below, O is the circumcentre of the triangle, and OA = 2 sqrt3 cm. Find the area of the triangle, in cm2.
Diagram: https://imgur.com/a/OIzeKyh
Answer by greenestamps(13208) (Show Source): You can put this solution on YOUR website!

Draw the radii of the circle to the three vertices of the equilateral triangle.

Segment OA, the segment from A to the vertex at one end of the side of the triangle containing A, and the radius of the circle to that same vertex, form a 30-60-90 right triangle.

Given leg OA = 2*sqrt(3), the other leg has length (2*sqrt(3))*sqrt(3) = 6.

The altitudes of an equilateral triangle divide each other in the ratio 2:1; that means OA is 1/3 the length of the altitude of the equilateral triangle. Given OA=2*sqrt(3), the altitude of the equilateral triangle is then 6*sqrt(3).

The area of the equilateral triangle is one-half base times height; that is

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