10. PRACTICE Find the area of an equilateral triangle with sides 6 cm .

To find the area of an equilateral triangle with sides of 6 cm, we can use the formula for the area of an equilateral triangle: \[ \text{Area} = \frac{\sqrt{3}}{4} \times \text{side}^2 \] Given that the side of the equilateral triangle is 6 cm, we can substitute this value into the formula to find the area: \[ \text{Area} = \frac{\sqrt{3}}{4} \times 6^2 \] Now, we can calculate the area of the equilateral triangle with sides of 6 cm. Calculate the value by following steps: - step0: Calculate: \(\frac{\sqrt{3}}{4}\times 6^{2}\) - step1: Rewrite the expression: \(\frac{\sqrt{3}}{4}\times 2^{2}\times 3^{2}\) - step2: Rewrite the expression: \(\frac{\sqrt{3}}{2^{2}}\times 2^{2}\times 3^{2}\) - step3: Reduce the numbers: \(\sqrt{3}\times 3^{2}\) - step4: Multiply: \(3^{2}\sqrt{3}\) - step5: Evaluate the power: \(9\sqrt{3}\) The area of the equilateral triangle with sides of 6 cm is approximately 15.588457 square centimeters.