The perimeter of an equilateral triangle is equal to the perimeter of a square whose diagonal is 6\sqrt{6} cm. Find the area of the equilateral triangle.

18\sqrt{3} cm²
38\sqrt{3} cm²
48\sqrt{3} cm²
28\sqrt{3} cm²

Correct answer: 48\sqrt{3} cm²

Solution

The diagonal of the square is \(6\sqrt{6}\), so its side is \(\frac{6\sqrt{6}}{\sqrt{2}}=6\sqrt{3}\) cm. Its perimeter is \(24\sqrt{3}\) cm, so each side of the equilateral triangle is \(8\sqrt{3}\) cm, giving area \(\frac{\sqrt{3}}{4}(8\sqrt{3})^2=48\sqrt{3}\) cm².

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