To solve the equation $A = \frac{1}{2} a p$ for $a$, follow these steps:

1. Start with the formula for the area of a regular polygon: $A = \frac{1}{2} a p$ where:

   • $A$ is the area,
   • $a$ is the apothem, and
   • $p$ is the perimeter.

2. Multiply both sides by 2 to eliminate the fraction: $2A = a p$

3. Finally, divide both sides by $p$ to solve for $a$: $a = \frac{2A}{p}$

The correct equation is: $a = \frac{2A}{p}$

Thus, the correct option is: $a = \frac{2A}{p}$.

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you find the perimeter of a regular polygon?
2. What is the significance of the apothem in a polygon?
3. How is the area of a regular polygon related to its side length?
4. How do you derive the formula for the area of a regular polygon?
5. What is the formula for the area of a polygon if you know the radius?

Tip: In a regular polygon, all sides and angles are equal, which simplifies many calculations involving area and perimeter.