Area of Trapezoid
Average of the parallel sides times height.
Key idea
Average of the parallel sides times height.
In depth
A trapezoid has one pair of parallel sides. Its area is the average of the parallel sides times the height: A = ½(a + b)h. Two copies placed together make a parallelogram with base a + b.
Worked example
Parallel sides 5 and 9, height 4: A = ½(14)(4) = 28.
Formula
Real-world uses
- Working out the area of a tapered wall, a road cross-section or a cross-section of a beam
Common mistake
Using a slanted side as the height.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Area of Trapezoid?
Average of the parallel sides times height. It is a topic at the intermediate level in Geometry.
What is the formula for Area of Trapezoid?
The key formula is A = ½(a+b)h.
Where is Area of Trapezoid used in real life?
Real-world examples: Working out the area of a tapered wall, a road cross-section or a cross-section of a beam.
What should I learn before Area of Trapezoid?
Make sure you are comfortable with Heron’s Formula, the previous topic in Geometry.
What is a common mistake with Area of Trapezoid?
Using a slanted side as the height.
How can I practise Area of Trapezoid?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Area of Trapezoid?
Move on to Area of Rhombus and Kite next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.