Base Area of a Trapezium
2026-02-28 14:07 Diff
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Last updated on October 28, 2025

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

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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.

Problem 1

The bases of a trapezium are 6 cm and 10 cm, and the height is 5 cm. Find the base area.

Okay, lets begin

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

Well explained 👍

Problem 2

A trapezium has bases of 8 cm and 12 cm, with a height of 6 cm. Find the base area.

Okay, lets begin

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

Well explained 👍

Problem 3

The height of a trapezium is 9 cm, and its bases are 5 cm and 15 cm. Find the base area.

Okay, lets begin

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

Well explained 👍

Problem 4

The base area is 56 cm², and the height is 8 cm. If one base is 4 cm, find the other base.

Okay, lets begin

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

Well explained 👍

Problem 5

A trapezium has an area of 75 cm², with bases of 9 cm and 11 cm. Find the height.

Okay, lets begin

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

Well explained 👍

FAQs on Base Area of a Trapezium

1.What is the base area of the trapezium?

The base area of a trapezium is the area enclosed by its four sides, calculated using: 1/2 × (Base1 + Base2) × Height.

2.What is the formula for the base area of a trapezium?

Area = 1/2 × (Base1 + Base2) × Height

3.What is the formula for the base area of a trapezium with equal bases?

If the bases are equal, the trapezium is a rectangle. Use Area = Base × Height.

4.Is the base area the same as the perimeter of a trapezium?

No, the base area is the space enclosed by the trapezium, while the perimeter is the total length around the shape.

5.What unit is used for the base area of the trapezium?

The units are always in square units like cm².

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.

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: She has songs for each table which helps her to remember the tables