Area of a Trapezoid – Formula, Examples & Practice Problems

What Is the Area of a Trapezoid?

The area of a trapezoid is the total amount of space inside the shape.

A trapezoid is a flat, four-sided shape that has two parallel sides. These two parallel sides are called the bases of the trapezoid — one is longer (the longer base) and one is shorter (the shorter base).

The height of a trapezoid is the straight vertical distance between the two bases. It is always measured at a right angle (90°) to the bases — not along the slanted side.

To find the area, you need to know three things:

• The length of the first base (a)
• The length of the second base (b)
• The height (h) of the trapezoid

Formula for the Area of a Trapezoid

The formula is:

Area = ½ × (a + b) × h

Or written another way:

Area = (a + b) / 2 × h

Where:

• a = length of the first base (top base)
• b = length of the second base (bottom base)
• h = height of the trapezoid

Why does this formula work?

Think of the trapezoid as an “average” of a rectangle. If you take the average of the two bases — (a + b) / 2 — that gives you the “middle width” of the shape. Then you multiply that middle width by the height, just like finding the area of a rectangle.

Important note about units:

• If the sides are measured in centimeters (cm), the area is in cm²
• If the sides are measured in meters (m), the area is in m²
• If the sides are measured in inches (in), the area is in in²

How to Calculate the Area of a Trapezoid – Step by Step

Follow these 4 simple steps every time:

Step 1: Identify the two bases (a and b) — the two parallel sides.

Step 2: Identify the height (h) — the perpendicular distance between the two bases.

Step 3: Add the two bases together: (a + b)

Step 4: Multiply by the height, then divide by 2: Area = (a + b) / 2 × h

Solved Examples

Example 1 – Basic Calculation

A trapezoid has a top base of 6 cm, a bottom base of 10 cm, and a height of 4 cm. What is its area?

Solution:

• a = 6 cm
• b = 10 cm
• h = 4 cm

Area = (a + b) / 2 × h

= (6 + 10) / 2 × 4

= 16 / 2 × 4

= 8 × 4

= 32 cm²

Example 2 – Finding Area When Height Is Given Separately

A trapezoid has bases of 5 m and 9 m. The height is 3 m. Find the area.

Solution:

= (5 + 9) / 2 × 3

= 14 / 2 × 3

= 7 × 3

= 21 m²

Example 3 – Working Backward (Finding a Missing Base)

The area of a trapezoid is 40 cm². One base is 6 cm and the height is 5 cm. What is the other base?

Solution:

Start with the formula: 40 = (6 + b) / 2 × 5

Divide both sides by 5: 8 = (6 + b) / 2

Multiply both sides by 2: 16 = 6 + b

Subtract 6: b = 10 cm

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Practice Questions

Try these on your own! Answers are listed below.

Question 1: A trapezoid has bases of 8 cm and 14 cm, and a height of 6 cm. What is the area?

Question 2: Find the area of a trapezoid with bases 3 in and 7 in, and height 5 in.

Question 3: A trapezoid has an area of 60 m². The two bases are 8 m and 12 m. What is the height?

Question 4: Both bases of a trapezoid are equal at 10 cm, and the height is 4 cm. What is the area? (Hint: What shape does this become?)

Question 5: A garden is shaped like a trapezoid. The two parallel sides measure 15 ft and 25 ft. The distance between them is 10 ft. What is the area of the garden?

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Answers:

1. 66 cm²
2. 25 in²
3. 6 m
4. 40 cm² (becomes a rectangle)
5. 200 ft²

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Frequently Asked Questions (FAQs)