The formula to calculate the perimeter of a parallelogram is given by

where $a$ and $b$ represent the lengths of two adjacent sides.

To elaborate, a parallelogram is a four-sided geometric figure characterized by having opposite sides that are both equal in length and parallel. To determine the perimeter, which is the total distance around the shape, you need to sum the lengths of all four sides. However, because opposite sides are equal, it suffices to know only the lengths of two adjacent sides, typically denoted as $a$ and $b$.

The formula $P = 2(a + b)$ operates on the principle that you are effectively adding the length of one pair of opposite sides twice. For instance, if one side $a$ measures $5 \text{ cm}$ and the adjacent side $b$ measures $7 \text{ cm}$, the perimeter can be calculated as follows:

This formula is particularly advantageous as it streamlines the process of calculating the perimeter, especially in more complex scenarios where only the lengths of two sides may be provided. It is important to remember that the defining characteristic of a parallelogram—where opposite sides are equal in length—facilitates the use of this formula. Once the lengths of the two adjacent sides are known, the lengths of the other two sides can be inferred immediately.