Formula for Perimeter of a Trapezoid

Perimeter of a Trapezoid Formula

The perimeter of a trapezoid is the total distance around its four sides. In a trapezoid, two opposite sides are parallel but of different lengths, while the other two sides are non-parallel.

To find the perimeter, you need the lengths of all four sides. Below is the formula for calculating the perimeter of a trapezoid, with a detailed explanation and examples.

Formula for the Perimeter of a Trapezoid

Using All Four Sides:

If the lengths of the four sides $a$, $b$, $c$, and $d$ are known,

The perimeter $P$ can be calculated with the formula:

$P=a+b+c+d$

In this formula:

• $a$ and $b$ are the lengths of the two parallel sides (bases) of the trapezoid
• $c$ and $d$ are the lengths of the non-parallel sides (legs) of the trapezoid

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Detailed Explanation of the Formula

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Understanding the Formula

The formula $P=a+b+c+d$ calculates the perimeter of a trapezoid by simply adding the lengths of all four sides. This method is straightforward and requires knowing the lengths of both parallel and non-parallel sides of the trapezoid.

Example 1: Calculating Perimeter with Given Side Lengths

Problem: Find the perimeter of a trapezoid with side lengths $a=12\text{cm}$, $b=8\text{cm}$, $c=5\text{cm}$, and $d=7\text{cm}$.

Solution:

1. Write down the formula: $P=a+b+c+d$.
2. Substitute the given values: $P=12+8+5+7$.
3. Add the side lengths: $P=32\text{cm}$.

The perimeter of the trapezoid is $32\text{cm}$.

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Example 2: Finding a Missing Side Length from Perimeter

Problem: A trapezoid has a perimeter of $P=40\text{cm}$, with side lengths $a=15\text{cm}$, $b=10\text{cm}$, and $c=8\text{cm}$. Find the length of the fourth side $d$.

Solution:

1. Start with the perimeter formula: $P=a+b+c+d$.
2. Substitute $P=40$, $a=15$, $b=10$, and $c=8$: $40=15+10+8+d$.
3. Simplify: $40=33+d$.
4. Subtract 33 from both sides to solve for $d$: $d=7\text{cm}$.

The length of the fourth side $d$ is $7\text{cm}$.

These examples demonstrate how to calculate the perimeter of a trapezoid or find an unknown side length based on the perimeter formula $P=a+b+c+d$.