How To Find The Perimeter Of An Isosceles Trapezium/Trapezoid

An isosceles trapezium (or trapezoid) is a special type of trapezoid where the non-parallel sides (legs) are equal in length. Calculating the perimeter of an isosceles trapezium is straightforward using the formula that sums the lengths of all its sides.

Formula to Find the Perimeter of an Isosceles Trapezium

The perimeter $P$ of an isosceles trapezium ABCD, where $AD$ and $BC$ are the equal sides, can be calculated using the following formula:

$$P=AB+CD+2\cdot AD$$

Alternatively:

$$P=AB+CD+2\cdot BC$$

Where:

- $P$ represents the perimeter of the trapezium.

- $AB$ and $CD$ are the lengths of the parallel sides (bases).

- $AD$ and $BC$ are the lengths of the non-parallel sides (legs).

Explanation of the Formula

The formula $P=AB+CD+2\cdot AD$ or $P=AB+CD+2\cdot BC$ is derived from the fact that the perimeter is the total length around the figure. Since $AD$ and $BC$ are equal in an isosceles trapezium, we multiply one of them by 2 to account for both sides.

Step-by-Step Calculation

Let's go through an example to illustrate how to use this formula.

Example:

Given an isosceles trapezium ABCD with the following side lengths:

- $AB=10$ units

- $CD=14$ units

- $AD=BC=7$ units

We want to find the perimeter of the trapezium.

Step 1: Identify the Given Values

Given:

- $AB=10$ units

- $CD=14$ units

- $AD=BC=7$ units

Step 2: Substitute the Values into the Formula

Using the formula $P=AB+CD+2\cdot AD$:

$$P=10+14+2\cdot 7$$

Step 3: Calculate the Perimeter

First, multiply the length of the legs by 2:

$$2\cdot 7=14$$

Then sum the values:

$$P=10+14+14$$

$$P=38$$

Final Value

The perimeter of an isosceles trapezium ABCD with side lengths $AB=10$ units, $CD=14$ units, and $AD=BC=7$ units is 38 units.

Using this simple formula, you can quickly determine the perimeter of any isosceles trapezium, making it a useful tool for various applications in geometry and real-life scenarios.