14) Find the exact area of an equilateral triangle whose sides are 8 in. a) \( \frac{8}{3} \sqrt{3} \mathrm{in}^{2} \)

To find the area of an equilateral triangle with side length \( s \), we can use the formula: \[ \text{Area} = \frac{\sqrt{3}}{4} s^2 \] Given that the side length \( s = 8 \) inches, we can substitute this value into the formula: \[ \text{Area} = \frac{\sqrt{3}}{4} (8)^2 \] Calculating \( (8)^2 \): \[ (8)^2 = 64 \] Now substituting this back into the area formula: \[ \text{Area} = \frac{\sqrt{3}}{4} \times 64 \] Simplifying this: \[ \text{Area} = 16\sqrt{3} \text{ in}^2 \] Thus, the exact area of the equilateral triangle is: \[ \text{Area} = 16\sqrt{3} \text{ in}^2 \] The answer provided in the question, \( \frac{8}{3} \sqrt{3} \text{ in}^2 \), is incorrect. The correct area is: \[ \boxed{16\sqrt{3} \text{ in}^2} \]