How to Calculate the Area of Trapezoids? (+FREE Worksheet!)
Picture a trapezoid like a slice of bread sitting on its short edge with the wider crust at the top. To find its area, you average the two parallel sides (the bases), then multiply that average by the height between them. In plain steps: add the two bases, multiply by the height, then divide by 2. The height has to be the straight perpendicular distance, not the slanted side. Once you see the formula as just an average times a height, trapezoids stop being intimidating.
Key takeaways:
- A trapezoid has exactly one pair of parallel sides (the bases).
- Area formula: \(A = \dfrac{1}{2}(b_1 + b_2)h\).
- Height is the perpendicular distance between the two parallel sides - not a slanted side.
- Add the two bases first, then multiply by the height, then halve.
- The same formula handles trapezoids in any orientation.
Learn more about trapezoids and how to calculate their areas by using the trapezoid area formula.
Watch this practice video for additional examples and reinforcement:
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A step-by-step guide to calculating the area of Trapezoids
- A quadrilateral with at least one pair of parallel sides is a trapezoid.
- Area of a trapezoid \(= \color{blue}{\frac{1}{2} h(b_{1}+b_{2})}\)
Area of Trapezoids, Example 1:
Calculate the area of the trapezoid.
For education statistics and research
Use trapezoid area formula: \(A= \frac{1}{2} h(b_{1}+b_{2 }) \)
\(b_{1}=14 cm, b_{2}=18\) \(cm\) and \(h=20\) \(cm\)
Then: \(A= \frac{1}{2}(20)(14+18)=10(32)=320\) \(cm^2\)
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Area of Trapezoids, Example 2:
Calculate the area of the trapezoid.
Solution:
Use trapezoid area formula: \(A= \frac{1}{2} h(b_{1}+b_{2 }) \)
\(b_{1}=12 cm, b_{2}=16\) \(cm\) and \(h=18\) \(cm\)
Then: \(A= \frac{1}{2}(18)(12+16)=9(28)=252\) \(cm^2\)
Exercises for Calculating Area of Trapezoids
Calculate the area for each trapezoid.
Download Trapezoids Worksheet
- \(\color{blue}{28 \ cm^2}\)
- \(\color{blue}{100 \ m^2}\)
- \(\color{blue}{66 \ ft^2}\)
- \(\color{blue}{96 \ cm^2}\)
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For a deeper walk through every geometry skill from the ground up, Geometry for Beginners covers angles, area, volume, triangles, and transformations with worked examples and plenty of practice. For algebra-heavy geometry topics, the companion Algebra I for Beginners ties the coordinate-plane work back to linear equations.
Frequently Asked Questions
What is the area formula of a trapezoid?
The area of a trapezoid is A = ½(b₁ + b₂)h, where b₁ and b₂ are the two parallel sides and h is the perpendicular height. In words: average the bases, then multiply by the height. For bases of 6 and 10 units with height 4, A = ½(16)(4) = 32 square units.
How do you calculate a trapezoid’s area?
Add the two parallel bases, multiply by the height, then divide by 2. For a garden bed with bases 9 m and 5 m and a height of 6 m, 9 + 5 = 14, 14 × 6 = 84, and 84 ÷ 2 = 42 m². Use the straight up-and-down height, not a slanted leg, and give the answer in square units.
Can trapezoids be parallelograms?
It depends on the definition your class uses. Under the exclusive definition, a trapezoid has exactly one pair of parallel sides, so a parallelogram is not a trapezoid. Under the inclusive definition, a trapezoid has at least one pair, so every parallelogram counts as a trapezoid. Either way, the area formula ½(b₁ + b₂)h still gives the right area.
Can trapezoids have right angles?
Yes. A right trapezoid has one leg perpendicular to both bases, which gives it two right angles. That leg is also the height, which makes the area easy: with bases 8 cm and 12 cm and a perpendicular leg of 5 cm, A = ½(8 + 12)(5) = 50 cm².
Are trapezoids and trapeziums the same?
They name the same shape in different countries. In the United States, a trapezoid is a quadrilateral with one pair of parallel sides. In British English that shape is called a trapezium. To add to the confusion, some American books use trapezium for a quadrilateral with no parallel sides, so check which convention your textbook follows.
What are examples of trapezoids in real life?
Trapezoids show up wherever something is wider at one end than the other: the sides of a popcorn box, many handbags, a lampshade seen from the side, the cross-section of a drainage ditch, and some bridge supports. Finding the area of a trapezoid-shaped yard or deck uses the same formula, ½(b₁ + b₂)h.
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If a topic on this page feels rusty, these short lessons go deeper:
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