Area and Perimeter of a Trapezoid: Formula, Examples, and Common Mistakes

After rectangles, squares, triangles, circles, and parallelograms, the trapezoid is the next shape to master. You'll spot trapezoids in real life all the time — in bridge supports, handbags, roof sections, and plots of land. It's a favorite topic in school geometry exams around the world, and once you understand the formula, it's easy to apply.

A quick note on names: in the United States and Canada this shape is called a trapezoid, while in the UK, Bangladesh, India, Australia and many other countries it is called a trapezium. They mean the same shape.

What Is a Trapezoid?

A trapezoid is a four-sided shape (quadrilateral) with:

• At least one pair of parallel sides, called the bases
• Two other sides, called the legs, which are not parallel

To calculate the area of a trapezoid, you need three measurements:

• Base 1 (b₁): one of the parallel sides
• Base 2 (b₂): the other parallel side
• Height (h): the perpendicular distance between the two bases

Area of a Trapezoid 

The area of a trapezoid tells you how much surface it covers.

Formula:

Area = ½ × (b₁ + b₂) × h

Or simply: A = (b₁ + b₂) × h ÷ 2

Here's an easy way to remember it: add the two parallel sides, find their average (divide by 2), then multiply by the height. In other words, a trapezoid's area equals the average of its two bases multiplied by its height.

Example 1:

A trapezoid has bases of 8 cm and 12 cm, and a height of 5 cm. Find its area.

• Area = (b₁ + b₂) × h ÷ 2
• Area = (8 + 12) × 5 ÷ 2
• Area = 20 × 5 ÷ 2
• Area = 100 ÷ 2
• Area = 50 cm²

As always, area is measured in square units (cm², m², ft²).

Perimeter of a Trapezoid

The perimeter is the total distance around all four sides of the trapezoid.

Formula:

Perimeter = base 1 + base 2 + leg 1 + leg 2

Or simply: P = b₁ + b₂ + c + d

Notice that the perimeter formula needs the two legs, but the area formula does not use them at all. The height is not the same as a leg, unless the leg happens to stand straight up at a right angle.

Example 2:

A trapezoid has bases of 8 cm and 12 cm, and legs of 5 cm and 6 cm. Find its perimeter.

• Perimeter = b₁ + b₂ + c + d
• Perimeter = 8 + 12 + 5 + 6
• Perimeter = 31 cm

Perimeter is measured in linear units (cm, m, ft).

Area vs. Perimeter: What's the Difference?

Area:

• What it measures: the space inside the trapezoid
• Formula: (b₁ + b₂) × h ÷ 2
• Unit: square units (cm², m²)
• What you need: both bases and the perpendicular height

Perimeter:

• What it measures: the distance around the trapezoid
• Formula: b₁ + b₂ + c + d
• Unit: linear units (cm, m)
• What you need: the lengths of all four sides

In short, area tells you how much space is inside the trapezoid, while perimeter tells you how far it is around the outside.

Common Mistakes Students Make

• Using a slanted leg instead of the perpendicular height. The height must always be measured at a right angle to the bases. A slanted leg is longer than the height, so using it gives a wrong area.
• Forgetting to divide by 2. A common error is to write (b₁ + b₂) × h and stop there. Always divide by 2 at the end.
• Adding only the two bases for perimeter. Perimeter needs all four sides, including both legs.
• Mixing up the bases with the legs. The bases are the parallel sides. Check which pair is parallel before you start.
• Dropping the square unit for area. Writing "50 cm" instead of "50 cm²" is a frequent mistake in written exams.

Practice Problem

Try this one yourself before checking the answer:

A field is shaped like a trapezoid. Its parallel sides measure 18 meters and 26 meters, and the perpendicular distance between them is 10 meters. Its two other sides measure 11 m and 12 m. Find both its area and perimeter.

Click to see the answer

• Area = (18 + 26) × 10 ÷ 2 = 44 × 10 ÷ 2 = 440 ÷ 2 = 220 m²
• Perimeter = 18 + 26 + 11 + 12 = 67 m

Quick Recap

• Area = ½ × (b₁ + b₂) × h — measured in square units, using the perpendicular height
• Perimeter = b₁ + b₂ + c + d — the sum of all four sides, in linear units
• The bases are the parallel sides, and the height is always measured at a right angle to them

With rectangles, squares, triangles, circles, parallelograms, and now trapezoids covered, you have a strong foundation in the most commonly tested 2D shapes. From here, you can move on to the rhombus, and then to 3D shapes like cubes, cylinders, and spheres.