# Find the area of a regular triangle of radius 2√2 inscribed in a circle.

August 31, 2021 | education

| To find out the area of the specified regular triangle, we will use the formula: S = a * b * c / 4R = a ^ 3 / 4R = (3R / √3) ^ 3 / 4R = 27R ^ 3 / (4R * √33) = 27R2 / (4 * 3 * √3) = 9R ^ 2 / (4 * √3), where R is the radius of the circumscribed circle (R = 2 * √2 units).

Let’s calculate: S = 3R ^ 2 / (4 * √3) = 9 * (2 * √2) ^ 2 / (4 * √3) = 9 * 4 * 2 / (4 * √3) = 9 * 2 / √3 = 18 / √3 units2 ≈ 10.39 units2.

Answer: The area of the indicated regular triangle is 10.39 units2.

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