How to Find the Area of a Trapezium Step by Step
The concept of Area of Trapezium Formula plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. By understanding this formula, students can calculate the space covered by trapezium-shaped land plots, tiles, or any geometry problem with confidence.
What Is Area of Trapezium Formula?
A trapezium (also known as a trapezoid in some countries) is a four-sided, closed figure or quadrilateral which has exactly one pair of parallel sides. The two parallel sides are called “bases” and the other two non-parallel sides are called “legs.” You’ll find this concept applied in topics such as area of parallelogram, land measurements, and architecture.
Key Formula for Area of Trapezium
Here’s the standard formula for finding the area of a trapezium (trapezoid):
Area = (1/2) × (Sum of Parallel Sides) × Height
Or, if the lengths of the parallel sides are a and b, and the height (the distance between these sides) is h,
Area = ½ × (a + b) × h
Cross-Disciplinary Usage
The area of trapezium formula is not only useful in Maths but also plays an important role in Physics for motion graphs, Computer Science for graphics and design, and even logical reasoning in real life. Students preparing for board exams, JEE or NEET will come across this formula in various contexts.
Step-by-Step Illustration
- Write down the values given in the problem (lengths of both parallel sides, and height if given).
- Add the lengths of the parallel sides: (a + b).
- Multiply the sum by the height: (a + b) × h.
- Divide this result by 2 to get the area: [(a + b) × h] ÷ 2.
- Write the final answer with proper square units, like cm² or m².
Solved Examples on Area of Trapezium
Let’s solve a couple of questions step by step for better understanding:
Example 1: Find the area of a trapezium if the lengths of the parallel sides are 8 cm and 6 cm, and the height is 5 cm.
1. Lengths: a = 8 cm, b = 6 cm, h = 5 cm2. Add parallel sides: 8 + 6 = 14 cm
3. Multiply sum with height: 14 × 5 = 70 cm²
4. Divide by 2: 70 ÷ 2 = 35 cm²
Final Answer: Area = 35 cm²
Example 2: The parallel sides of a trapezium are 10 m and 14 m, and the distance between them is 9 m. What is its area?
1. a = 10 m, b = 14 m, h = 9 m2. Add: 10 + 14 = 24 m
3. Multiply: 24 × 9 = 216 m²
4. Divide by 2: 216 ÷ 2 = 108 m²
Final Answer: Area = 108 m²
Area of Trapezium When All Sides Are Given
Sometimes, you get the lengths of all four sides but not the height. In such cases, if you know the lengths of bases (a, b) and the two legs (c, d), you can first find the height using a variant of the Pythagoras theorem. For an isosceles trapezium:
Height formula:
h = √ (c² − [(b−a)²/4])
Then, use the area formula: Area = ½ × (a + b) × h
This approach helps in questions where only all sides are provided.
Speed Trick or Vedic Shortcut
When both parallel sides and height are easy numbers, find the average of the two parallel sides, then multiply with height:
Shortcut: Area = [(a + b)/2] × h
This saves time in exams! Vedantu’s expert Maths teachers often use such speed methods in live classes.
Try These Yourself
- Find the area of a trapezium with parallel sides 12 cm and 15 cm, and height 8 cm.
- If the non-parallel sides of a trapezium are both 5 cm, and parallel sides are 20 cm and 10 cm, with the height missing, how would you find the area?
- A field is in the shape of a trapezium with bases 24 m and 36 m, and height 10 m. What is its area?
Frequent Errors and Misunderstandings
- Mixing up which two sides are parallel — always check the diagram!
- Forgetting to divide by 2 after multiplying with height.
- Missing unit conversion (cm to m, etc.).
- Using wrong values for height (must be perpendicular height).
Relation to Other Concepts
The area of trapezium formula is linked to concepts like area of quadrilateral, area and perimeter, and trapezoids. Once you understand this formula, problems related to composite areas and surface calculations become easier to solve!
Classroom Tip
A quick way to remember the formula: “Sum the bases, multiply by height, and take half!” Vedantu’s Maths classes often use memory rhymes and real-world scenarios (like plotting land) to make this concept stick in your mind during exams.
We explored area of trapezium formula—from definition, formula, stepwise methods, examples, common errors, and connections to other geometry topics. Keep practicing with Vedantu’s resources and live coaching to master all mensuration problems with ease!
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