Question \( 1-2 \) Look st the equation \[ V=\frac{3 \sqrt{3}}{2} a^{2} h \] The equation represents the volume of a night regular hexagonal prism where each edge of the hexa a, by rearranging the equation shown? \( a=\frac{\sqrt{2 V}}{3 \sqrt{3 h}} \) \( a=\frac{\sqrt{2 V h}}{3 \sqrt{3 h}} \) \( a=\sqrt{\frac{2 V}{3 \sqrt{3 h}}} \)

To solve for \( a \) in the equation for the volume of a right regular hexagonal prism: \[ V = \frac{3 \sqrt{3}}{2} a^{2} h \] **Step-by-Step Solution:** 1. **Start with the original equation:** \[ V = \frac{3 \sqrt{3}}{2} a^{2} h \] 2. **Isolate \( a^{2} \):** Multiply both sides by \( \frac{2}{3 \sqrt{3}} \): \[ a^{2} = \frac{2V}{3 \sqrt{3} h} \] 3. **Take the square root of both sides to solve for \( a \):** \[ a = \sqrt{\frac{2V}{3 \sqrt{3} h}} \] **Final Answer:** \[ a = \sqrt{\frac{2V}{3 \sqrt{3} h}} \] This corresponds to the **third option** provided: \[ a = \sqrt{\frac{2 V}{3 \sqrt{3} h}} \]