How To Calculate The Perimeter Of A Parallelogram ABCD

Calculating the perimeter of a parallelogram ABCD can be done easily using a simple formula. This article will guide you through the process using the formula $P=2\cdot (AB+AD)=2\cdot AB+2\cdot AD$, where $AB=DC$ and $AD=BC$. We will explain the formula and provide a step-by-step example to illustrate the calculations.

The Formula for the Perimeter of a Parallelogram

The perimeter $P$ of a parallelogram is calculated by:

$$P=2\cdot (AB+AD)=2\cdot AB+2\cdot AD$$

Where:

- $P$ is the perimeter of the parallelogram.

- $AB$ and $DC$ are the lengths of one pair of opposite sides.

- $AD$ and $BC$ are the lengths of the other pair of opposite sides.

Explanation of the Formula

$2\cdot (AB+AD)$: This part of the formula adds the lengths of adjacent sides $AB$ and $AD$, then multiplies by 2 to account for both pairs of opposite sides.

$2\cdot AB+2\cdot AD$: This is an alternative way to express the same calculation, showing the perimeter as the sum of twice the lengths of both pairs of opposite sides.

Step-by-Step Calculation

Let's work through an example to illustrate the process.

Example:

Suppose we have a parallelogram ABCD with:

- Side $AB=8$ units

- Side $AD=5$ units

We want to find the perimeter of the parallelogram.

Step 1: Identify the Given Values

Given:

- $AB=8$ units

- $AD=5$ units

Step 2: Substitute the Given Values into the Formula

$$P=2\cdot (8+5)=2\cdot 8+2\cdot 5$$

Step 3: Calculate the Perimeter

First, calculate the sum inside the parentheses:

$$8+5=13$$

Then, multiply by 2:

$$2\cdot 13=26$$

Alternatively, calculate each term separately and add them:

$$2\cdot 8=16$$

$$2\cdot 5=10$$

$$16+10=26$$

Final Value

For a parallelogram with sides $AB=8$ units and $AD=5$ units, the perimeter is 26 units.

This straightforward method for calculating the perimeter of a parallelogram ensures accurate results and is practical for various applications.