The area of a trapezium helps us measure how much two-dimensional space is enclosed inside a four-sided figure with one pair of parallel sides. Whether you’re solving geometry questions, measuring land, or working on design layouts, this formula makes calculations quick and reliable. It’s widely used in school mathematics and competitive exams because of its simplicity and real-life applications.
Formula for Calculating the Area of a Trapezium – Overview
| Formula | Variables & Meaning | When It Is Used |
|---|---|---|
| Area = ½ × (a + b) × h | a = first parallel side, b = second parallel side, h = height | When two parallel sides and the height are known |
What is the Area of a Trapezium in Maths?
In mathematics, the area of a trapezium represents the total surface covered by the quadrilateral that has exactly one pair of parallel sides. The area tells us how much space lies inside the shape and is always written in square units such as cm² or m².
To calculate this area, we take the average of the two parallel sides and multiply it by the perpendicular height. The height is always measured at a right angle between the parallel sides. The formula works well because a trapezium can be visualized as the combination of a rectangle and a triangle.
This method is very useful in everyday calculations like measuring irregular land plots, designing roads or bridges, and solving geometry questions in CUET, SSC, JEE, Banking, and school exams.
Examples to Calculate the Area of a Trapezium
Example 1: a = 10 cm, b = 6 cm, h = 5 cm
Step 1: Formula = ½ × (a + b) × h
Step 2: Area = ½ × (10 + 6) × 5
Step 3: Area = ½ × 16 × 5
Result: 40 cm²
So, the area of the trapezium is 40 cm².
Example 2: a = 12 cm, b = 8 cm, h = 7 cm
Step 1: Formula = ½ × (a + b) × h
Step 2: Area = ½ × (12 + 8) × 7
Step 3: Area = ½ × 20 × 7
Result: 70 cm²
So, the area of the trapezium is 70 cm².
FAQs about Area of a Trapezium Formula
Q1. What is a trapezium?
A trapezium is a quadrilateral with exactly one pair of opposite sides parallel.
Q2. Can I calculate the area without the height?
No, height is essential, but it can sometimes be found using Pythagoras theorem if slant sides are known.
Q3. Is trapezium the same as trapezoid?
Yes, the term is different across regions—British English uses trapezium; American English uses trapezoid.
Q4. What are the units for the area of a trapezium?
The area is always measured in square units like cm², m², or km².
Q5. Where is this formula used in real life?
In land measurement, construction, farming, road design, architecture, and exam problems.
Q6. Can a trapezium be a square?
No, because a square has two pairs of parallel sides, while a trapezium has only one.