Perimeter of Trapezoid - Definition, Formula, and Examples

What is Perimeter of Trapezoid?

The perimeter of a trapezoid is the total distance around the outside of the object. Picture a trapezoid-shaped field that you wish to erect a fence around. The perimeter is the length of the wire you need for that fence.

A trapezoid is a quadrilateral with at least one pair of parallel sides. The bases are the sides that are parallel, while the legs are the sides that are not parallel. You only need the lengths of the four boundary lines to get the perimeter. You don't need to bother about the height or the area.

Properties to Remember

• It is a two-dimensional shape that is closed.

• There are four sides and four corners.

• The sum of all interior angles is always 360 degrees.

• The perimeter is measured in linear units like centimetres (cm), meters (m), or inches (in).

Perimeter of Trapezoid Formula

Adding up the lengths of all the sides of a polygon will give you its boundaries. The formula follows this exact rule. It becomes quite easy to do the maths if we call the four sides of the trapezium a, b, c, and d.

The Formula:

Perimeter (P) = a + b + c + d

In this case:

• a and b are the lengths of the bases (the sides that are parallel).

• The lengths of the legs, c and d, are not parallel.

Formula Breakdown Table

To help students understand the formula better, below is a breakdown of it:

This formula makes sure that every part of the outer boundary is taken into account.

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How to Calculate Perimeter of Trapezoid 

It's important to know the formula, but it's much more important to use it accurately on tests. Follow these simple procedures to avoid making mistakes when you want to find the perimeter of a trapezoid

1. Find the lengths of the sides: Look at the picture or the problem with words. Write down how long each of the four sides is. Make sure they are all in the same unit, like cm.

2. Look for Missing Sides: For example, in an isosceles trapezoid, only one leg length might be specified because both legs are the same length.

3. Apply the Addition Rule: Add the four values together to get the answer.

4. Assign Units: Always include the right unit of measurement when you compose the final answer.

Example Scenario:

If a trapezium has bases that are 10 cm and 15 cm long and legs that are 7 cm and 8 cm long, you can find the area by doing this:

P = 10 + 15 + 7 + 8 = 40 cm.

Read More - Perimeter of a Circle – Definition, Formula, πd & 2πr with Examples

Types and the Perimeter of Trapezoid

The overall formula for finding the perimeter of a trapezoid is always the sum of its four sides. However, different forms of trapezoids have their own unique features that could affect how you solve the problems.

1. Isosceles Trapezoid

In an isosceles trapezoid, the legs, or non-parallel sides, are the same length.

• Formula: P = a + b + 2c (where 'c' is the length of one leg).

2. Scalene Trapezoid

In a scalene trapezoid, all four sides have different lengths. You must have the measurement for every single side to find the perimeter of the trapezoid correctly.

3. Right Trapezoid

A right trapezoid has two right angles. While this helps in finding the area or height, for the perimeter, you still just add the four sides provided.

Read More - Perimeter of a Sector – Formula, Definition, Types & Examples

Perimeter of Trapezoid Worksheet 

The greatest approach to get better at mental maths is to use real numbers. You can use these examples as a test to see how much you know.

Problem 1: The sides of a trapezoid are 12 m and 18 m long and run parallel to each other. The sides that aren't parallel are 5 m and 6 m. Find the total length of the boundary.

• Solution: Sum of sides = 12 + 18 + 5 + 6
  Perimeter of the trapezoid = 41 m.

Problem 2: The bases of an isosceles trapezoid are 8 cm and 12 cm. The length of each leg is 5 cm. Find the perimeter.

• Solution: P = 8 + 12 + 5 + 5
  P = 30 cm.

Problem 3: Find the side that is missing. The trapezoid's sides add up to 50. The three sides are 10, 15, and 12 units long.

• Solution: Missing side = 50 - (10 + 15 + 12)
  Missing side = 50 - 37 = 13 units.

Common Mistakes When Finding the Perimeter of Trapezoid

Students commonly make mistakes, even if the technique is easy. This is how to stay sharp:

• Mistaking height for side length: The height (the distance between the bases that is perpendicular to the bases) is utilised for area, not perimeter. Don't ever add the height to your trapezoid perimeter total unless the height is one of the sides (like in a right trapezoid).

• Mixing units: If one side is in mm and the others are in cm, change them all to cm first.

• Forgetting a Side: A trapezium always has four sides. If you only see three numbers, make sure it's an isosceles trapezium with two sides that are the same length.

If you follow these guidelines, you can be sure that you can solve any mathematical problem in your head or on a worksheet.

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