The altitude drawn from a vertex of an equilateral triangle to the opposite side measures 6√3 cm. Find the exact area of the triangle in cm².

Question

Accepted Answer

36√3. For a side a, the altitude is (√3/2)a. So (√3/2)a = 6√3 gives a = 12 cm. Area = (√3/4)a² = (√3/4) × 144 = 36√3 cm².

The altitude drawn from a vertex of an equilateral triangle to the opposite side measures 6√3 cm. Find the exact area of the triangle in $cm^{2}$ .