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# Area of a trapezium / trapezoid
- URL: https://www.esheets.io/area-of-a-trapezium-trapezoid/
- Published: 2025-03-29T21:17:54.000Z
- Updated: 2026-06-21T16:35:22.000Z
- Author: Richard Linnington
- Tags: Maths, Geometry and Shape

Trapezium? Trapezoid? You might not realise it but - regardless of which country you're from - the area of this polygon comes in handy more often than you'd think—like when calculating the surface of a sloped roof or the shape of a skate ramp. Trapeziums pop up in design, engineering, and architecture, so learning how to find their area is a clever bit of maths with real-world power! [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise area of a trapezium with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Identifying the two parallel sides.
- Identifying the perpendicular height.
- Using area = 1/2 × (a + b) × h.
- Giving the answer in square units.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Calculate the area of each trapezium/trapezoid below.

## Topic guide

### What this worksheet practises

This worksheet provides practice on calculating the area of a trapezium. This is a common shape in geometry problems and real-world applications. A trapezium is a quadrilateral with exactly one pair of parallel sides. Understanding how to find its area is a key progression from finding the area of simpler shapes like rectangles and triangles.

### Key method

The standard formula for the area of a trapezium is: Area = ½(a + b)h, where 'a' and 'b' are the lengths of the parallel sides, and 'h' is the perpendicular height between them.

- Identify the two parallel sides. These are 'a' and 'b'.
- Identify the perpendicular height 'h'. Ensure it is at a right angle (90 degrees) to the parallel sides, not a slanted edge.
- Add the lengths of the parallel sides together first.
- Multiply that sum by the height.
- Finally, halve the result.

### Worked example

**Find the area of a trapezium with parallel sides of 6 cm and 10 cm, and a perpendicular height of 4 cm.**

Step 1: Write out the formula and substitute your values.

Area = ½(6 + 10) × 4

Step 2: Calculate the brackets first.

6 + 10 = 16

Step 3: Multiply by the height.

16 × 4 = 64

Step 4: Halve the result.

½ of 64 = 32

The area is 32 cm².

### Common mistakes to avoid

A very common mistake is using the slanted side length instead of the perpendicular height. Always look for the line that forms a right angle with the parallel base. Additionally, remember the order of operations: you must add the parallel sides together *before* multiplying by the height.

### How to check your answer

Think about the area of rectangles. If your trapezium has bases of 6 and 10, the "average" width is 8\. A rectangle of width 8 and height 4 would have an area of 32, which matches our calculation. If your answer is wildly different, check your steps.