Area of a Trapezoid

How to area of a trapezoid, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

A trapezoid (also called a trapezium) is a four-sided polygon with exactly one pair of parallel sides called the bases. Finding its area requires one formula that averages the two bases, then multiplies by the height. This is a standard GED geometry topic that appears in both computation and word-problem formats.

What Is a Trapezoid?

A trapezoid is a quadrilateral with exactly one pair of parallel sides. The two parallel sides are called the bases (b₁ and b₂). The perpendicular distance between the bases is the height (h). The non-parallel sides are called the legs.

GED Math for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the GED Math Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.34 out of 5 based on 106 customer ratings

Satisfied 92 Students

Area Formula

A = ½ × \(\color{blue}{(b<\text{ sub }>1 + b<\text{ sub }>2) \times h}\)

• b₁ = length of the first (shorter or longer) base
• b₂ = length of the second base
• h = perpendicular height between the two bases

Why does this work? A trapezoid can be split into two triangles, each sharing the height. Adding their areas gives \(\color{blue}{\frac{1}{2}b_{1}h + \frac{1}{2}b_{2}h = \frac{1}{2}(b_{1} + b_{2})h}\).

How to Use the Formula

Identifying bases and height

The two bases are the parallel sides. The height is always measured perpendicular to the bases, not along the slanted legs.

Applying the formula

1. Add the two bases: \(\color{blue}{b_{1} + b_{2}}\).
2. Multiply by the height: \(\color{blue}{(b_{1} + b_{2}) \times h}\).
3. Divide by 2: \(\color{blue}{\frac{1}{2} \times (b_{1} + b_{2}) \times h}\).

Step-by-Step Summary

1. Identify the two parallel bases and the perpendicular height.
2. Add the two bases.
3. Multiply the sum by the height.
4. Divide by 2 and label with square units.

Watch: Area of a Trapezoid (Video Lesson)

Math with Mr. J demonstrates the trapezoid area formula with clear, step-by-step examples:

Worked Examples

Example 1: Find the area of a trapezoid with bases 4 cm and 8 cm and height 5 cm.

\(\color{blue}{A = \frac{1}{2} \times (4 + 8) \times 5 = \frac{1}{2} \times 12 \times 5 = \frac{1}{2} \times 60 = 30 \text{ cm }^{2}}\)

Example 2: A trapezoid has bases 6 m and 10 m and a height of 4 m. Find the area.

\(\color{blue}{A = \frac{1}{2} \times (6 + 10) \times 4 = \frac{1}{2} \times 16 \times 4 = \frac{1}{2} \times 64 = 32 m^{2}}\)

Example 3: A trapezoidal garden has parallel sides of 3 yd and 7 yd with a perpendicular height of 6 yd. How many square yards of grass are needed?

\(\color{blue}{A = \frac{1}{2} \times (3 + 7) \times 6 = \frac{1}{2} \times 10 \times 6 = \frac{1}{2} \times 60 = 30 \text{ yd }^{2}}\)

Example 4: The area of a trapezoid is 21 ft². The height is 3 ft and one base is 5 ft. Find the other base.

\(\color{blue}{21 = \frac{1}{2} \times (5 + b_{2}) \times 3 \rightarrow 21 = 1.5(5 + b_{2}) \rightarrow 14 = 5 + b_{2} \rightarrow b_{2} = 9 \text{ ft }}\)

More Practice: Area of a Trapezoid (Video)

Khan Academy explains the formula and works through additional geometry examples:

Exercises

1. Find the area of a trapezoid with bases 5 in. And 9 in. And height 3 in.
2. A trapezoid has bases 7 cm and 13 cm and height 6 cm. Find the area.
3. A trapezoidal roof section has parallel edges of 10 ft and 16 ft, with a perpendicular height of 8 ft. Find the area.
4. The area of a trapezoid is 45 cm². The two bases are 6 cm and 9 cm. Find the height.
5. A trapezoid has equal bases of 8 m each and height 5 m. What shape is it effectively, and what is the area?
6. Bases are 4 ft and 10 ft; height is 7 ft. Find the area.

Answers

1. \(\color{blue}{\frac{1}{2}(5+9)(3) = \frac{1}{2}\times 12\times 3 = 18 \text{ in }^{2}}\)
2. \(\color{blue}{\frac{1}{2}(7+13)(6) = \frac{1}{2}\times 20\times 6 = 60 \text{ cm }^{2}}\)
3. \(\color{blue}{\frac{1}{2}(10+16)(8) = \frac{1}{2}\times 26\times 8 = 104 \text{ ft }^{2}}\)
4. \(\color{blue}{45 = \frac{1}{2}(6+9)h \rightarrow 45 = 7.5h \rightarrow h = 6 \text{ cm }}\)
5. Equal bases mean it is a parallelogram (rectangle); \(\color{blue}{A = 8\times 5 = 40 m^{2}}\) (also confirmed by formula: ½\(\color{blue}{(8+8)(5) = 40}\))
6. \(\color{blue}{\frac{1}{2}(4+10)(7) = \frac{1}{2}\times 14\times 7 = 49 \text{ ft }^{2}}\)

Frequently Asked Questions

What is the trapezoid area formula?

The area of a trapezoid is A = ½ × (b₁ + b₂) × h, where b₁ and b₂ are the two parallel bases and h is the perpendicular height between them. In words, you average the two bases and multiply by the height. For bases of 7 and 11 with a height of 4, A = ½ × 18 × 4 = 36 square units.

How do you find the area of a trapezoid?

First identify the two parallel sides (the bases) and the height measured at a right angle to them. Add the bases, multiply by the height, then divide by 2. For a trapezoid with bases 5 cm and 9 cm and height 6 cm: 5 + 9 = 14, 14 × 6 = 84, 84 ÷ 2 = 42 cm². Do not use a slanted leg as the height.

How do you find trapezoid area without the height?

You need to work out the height from the side lengths first. For an isosceles trapezoid, subtract the bases, halve the result, and use the Pythagorean theorem with a leg. With bases 10 and 4 and legs of 5, the overhang is (10 − 4) ÷ 2 = 3, so h = √(5² − 3²) = 4. Then A = ½ × (10 + 4) × 4 = 28 square units.

Is trapezoid area squared?

Yes, trapezoid area is always given in square units, such as cm², in² or ft², because you multiply one length (the average of the bases) by another length (the height). If the bases are 3 ft and 5 ft and the height is 2 ft, the area is ½ × 8 × 2 = 8 ft². The bases and height must use the same unit before you multiply.

Is the area of a trapezoid the same as a rectangle?

Not in general, but a trapezoid has the same area as a rectangle whose width is the average of the two bases and whose height is the same. A trapezoid with bases 6 and 10 and height 5 has area ½ × 16 × 5 = 40, exactly the same as an 8 × 5 rectangle. If both bases are equal, the formula simply becomes base × height.

Can a trapezoid be a rectangle?

It depends on the definition you use. Many U.S. textbooks define a trapezoid as having exactly one pair of parallel sides, so a rectangle, which has two pairs, is not a trapezoid. Under the inclusive definition (at least one pair), every rectangle counts as a trapezoid. Either way, the trapezoid formula still works for a rectangle: ½ × (b + b) × h = b × h.

Related Topics

• Area of a Parallelogram
• Area of a Triangle
• Polygons
• Finding Area of Compound Figures
• Triangles