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102 LearnersLast updated on October 28, 2025
Base Area of a Trapezium
The base area of a trapezium refers to the area of the flat surface, which is a 2-dimensional shape. A trapezium (or trapezoid) is a quadrilateral with at least one pair of parallel sides.
What is the Base Area of a Trapezium?
The base area of a trapezium is simply the area enclosed by its four sides.
A trapezium is a 2-dimensional shape with one pair of parallel sides called bases and two non-parallel sides called legs.
The area of a trapezium is the total space enclosed by these sides.
What is the Base Area of a Trapezium Formula?
The formula for the area of a trapezium is given by: Area = 1/2 × (Base1 + Base2) × Height
In this formula, Base1 and Base2 are the lengths of the parallel sides, and the Height is the perpendicular distance between these sides.
How to Find the Base Area of a Trapezium?
The base area of a trapezium can be found using the formula: Area = 1/2 × (Base1 + Base2) × Height.
This formula can be used to find the base area by following these steps:
Step 1: First, determine the lengths of the two parallel sides (Base1 and Base2) and the height of the trapezium.
Step 2: Use the formula Area = 1/2 × (Base1 + Base2) × Height to find the area.
Step 3: Write the answer in square units.
For example, if the trapezium has bases of 5 cm and 7 cm, and the height is 4 cm, find the base area:
Area = 1/2 × (5 + 7) × 4 = 1/2 × 12 × 4 = 24 cm²
Tips and Tricks for Finding the Base Area of a Trapezium
Here are some tips and tricks that help solve the problem easily:
- Remember, a trapezium has two parallel sides.
- Identify the height correctly; it must be perpendicular to the bases.
- Use the right formula.
- Check the units.
- Don’t confuse with perimeter.
Common Mistakes and How to Avoid Them on the Base Area of a Trapezium
When finding the base area of the trapezium, students make small mistakes, which lead to the wrong answer. Here are some common mistakes that can be avoided.
Mistake 1
Confusing height with side length
Students often mistakenly use a slanted side as the height. Always ensure that the height is perpendicular to the bases.
Mistake 2
Using the wrong formula
Some students mix up the area with the perimeter formula. The area of a trapezium is calculated using the formula: 1/2 × (Base1 + Base2) × Height.
Mistake 3
Forgetting to divide by 2
First, sum the lengths of the parallel sides, then multiply by the height, and finally divide by 2 to find the base area.
Mistake 4
Misidentifying the parallel sides
Sometimes students use non-parallel sides as bases. Double-check that the bases are the parallel sides.
Mistake 5
Calculating only one base instead of using both
Students mistakenly use only one base in the formula. Always include both Base1 and Base2 in the calculation.
Solved Examples for Base Area of a Trapezium
Problem 1
The bases of a trapezium are 6 cm and 10 cm, and the height is 5 cm. Find the base area.
40 cm²
Explanation
To find the base area of the trapezium, use the formula: Area = 1/2 × (Base1 + Base2) × Height
Base1 = 6 cm, Base2 = 10 cm, Height = 5 cm
Area = 1/2 × (6 + 10) × 5
Area = 1/2 × 16 × 5
Area = 40 cm²
Problem 2
A trapezium has bases of 8 cm and 12 cm, with a height of 6 cm. Find the base area.
60 cm²
Explanation
To find the base area of the trapezium, use the formula: Area = 1/2 × (Base1 + Base2) × Height
Base1 = 8 cm, Base2 = 12 cm, Height = 6 cm
Area = 1/2 × (8 + 12) × 6
Area = 1/2 × 20 × 6
Area = 60 cm²
Problem 3
The height of a trapezium is 9 cm, and its bases are 5 cm and 15 cm. Find the base area.
90 cm²
Explanation
Base1 = 5 cm, Base2 = 15 cm, Height = 9 cm
Area = 1/2 × (5 + 15) × 9
Area = 1/2 × 20 × 9
Area = 90 cm²
Problem 4
The base area is 56 cm², and the height is 8 cm. If one base is 4 cm, find the other base.
10 cm
Explanation
To find the unknown base, use the formula: Area = 1/2 × (Base1 + Base2) × Height
56 = 1/2 × (4 + Base2) × 8
56 = 4 × (4 + Base2) 14 = 4 + Base2
Base2 = 14 - 4
Base2 = 10 cm
Problem 5
A trapezium has an area of 75 cm², with bases of 9 cm and 11 cm. Find the height.
5 cm
Explanation
To find the height, use the formula: Area = 1/2 × (Base1 + Base2) × Height
75 = 1/2 × (9 + 11) × Height
75 = 10 × Height
Height = 75 ÷ 10
Height = 7.5 cm
FAQs on Base Area of a Trapezium
1.What is the base area of the trapezium?
2.What is the formula for the base area of a trapezium?
3.What is the formula for the base area of a trapezium with equal bases?
4.Is the base area the same as the perimeter of a trapezium?
5.What unit is used for the base area of the trapezium?
Important Glossary for Base Area of a Trapezium
- Base Area: The area enclosed by the sides of a trapezium, calculated using 1/2 × (Base1 + Base2) × Height.
- Trapezium: A quadrilateral with at least one pair of parallel sides.
- Height: The perpendicular distance between the two parallel bases of a trapezium.
- Parallel Sides: The two opposite sides of a trapezium that are parallel to each other.
- Quadrilateral: A four-sided polygon.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
