EDEXCEL GCSE FOUNDATION MATHS - What is the Area of a Trapezium

Edexcel GCSE Foundation Maths: Area of a Trapezium

What is a Trapezium?

A trapezium is a quadrilateral (four-sided shape) with one pair of parallel sides. These parallel sides are called the bases of the trapezium, and the other two sides are called the legs.

Formula for the Area of a Trapezium

The area of a trapezium is calculated using the following formula:

Area = (1/2) * (sum of the bases) * (height) 

where:

• Area is the space enclosed by the trapezium
• Bases are the two parallel sides (a and b)
• Height is the perpendicular distance between the bases (h)

Example 1

Let's calculate the area of a trapezium with the following dimensions:

• Base a = 5 cm
• Base b = 8 cm
• Height h = 4 cm

Step 1: Find the sum of the bases: 5 cm + 8 cm = 13 cm Step 2: Multiply the sum of the bases by the height: 13 cm * 4 cm = 52 cm² Step 3: Divide the result by 2: 52 cm² / 2 = 26 cm²

Therefore, the area of the trapezium is 26 cm².

Example 2

Calculate the area of a trapezium with bases of 10 cm and 6 cm and a height of 5 cm.

Solution:

• Sum of bases: 10 cm + 6 cm = 16 cm
• Area: (1/2) * 16 cm * 5 cm = 40 cm²

Key Points

• Remember to use the perpendicular height. Don't use the length of the legs.
• Units: Make sure to include the correct units for area (e.g., cm², m²).
• Practice: Work through as many examples as you can to become confident in using the formula.

Practice Exercises

1. Calculate the area of a trapezium with bases of 7 cm and 9 cm and a height of 6 cm.
2. Find the area of a trapezium with bases of 12 m and 8 m and a height of 5 m.
3. A trapezium has a base of 15 cm, a height of 8 cm, and an area of 100 cm². Find the length of the other base.

By understanding the formula and practicing these exercises, you will be well-equipped to solve problems involving the area of a trapezium in your Edexcel GCSE Foundation Maths exam.