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.
