Perimeter of a Rhombus Formula
The perimeter of a rhombus is the total distance around its four equal sides. In a rhombus, all four sides have the same length, making the perimeter calculation straightforward if the length of one side is known.
In this guide, we will go through the formula for calculating the perimeter of a rhombus, with detailed explanations and examples.
Formula for the Perimeter of a Rhombus
Using Side Length:
If the length of one side \( a \) of the rhombus is known,
The perimeter \( P \) can be calculated with the formula:
\( P = 4a \)
In this formula:
- \( a \) is the length of any one side of the rhombus
Detailed Explanation of the Formula
Understanding the Formula
The formula \( P = 4a \) calculates the perimeter of a rhombus by multiplying the length of one side by 4, as all four sides in a rhombus are equal in length. This formula is useful when the side length is given or can be easily measured.
Example 1: Calculating Perimeter with Known Side Length
Problem: Find the perimeter of a rhombus with a side length of \( a = 7 \, \text{cm} \).
Solution:
- Write down the formula: \( P = 4a \).
- Substitute \( a = 7 \): \( P = 4 \times 7 \).
- Multiply: \( P = 28 \, \text{cm} \).
The perimeter of the rhombus is \( 28 \, \text{cm} \).
Example 2: Finding Side Length from Perimeter
Problem: A rhombus has a perimeter of \( P = 40 \, \text{cm} \). Find the length of one side.
Solution:
- Start with the perimeter formula: \( P = 4a \).
- Substitute \( P = 40 \): \( 40 = 4a \).
- Divide both sides by 4 to solve for \( a \): \( a = 10 \, \text{cm} \).
The length of each side of the rhombus is \( 10 \, \text{cm} \).
These examples demonstrate how to calculate the perimeter of a rhombus or find an unknown side length based on the perimeter formula \( P = 4a \).