Introduction
Calculating the area of a trapezium (or trapezoid) when you know the lengths of both bases and the height is crucial in geometry. In this guide, we'll explore the formula to calculate the area of a trapezium and provide step-by-step instructions to help you solve for the area.
Understanding the Trapezium
A trapezium, also known as a trapezoid in the US, is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases, and the distance between them is the height.
The Formula for the Area of a Trapezium
The area \( A \) of a trapezium can be found using the formula:
\[ A = \frac{(a + b) \times h}{2} \]
Where:
- \( a \) is the length of one base of the trapezium.
- \( b \) is the length of the other base of the trapezium.
- \( h \) is the height of the trapezium.
Explaining the Formula
The area formula for a trapezium involves taking the sum of the lengths of the two bases, multiplying by the height, and then dividing by 2. This formula essentially finds the average length of the bases and multiplies it by the height.
Step-by-Step Calculation
Let's work through an example to illustrate the process.
Example:
Suppose we have a trapezium with base \( a = 6 \) units, base \( b = 10 \) units, and height \( h = 8 \) units. We want to find the area of the trapezium.
Step 1: Identify the Given Values
Given:
- Base \( a = 6 \) units
- Base \( b = 10 \) units
- Height \( h = 8 \) units
Step 2: Use the Formula to Find the Area
Using the formula \( A = \frac{(a + b) \times h}{2} \), substitute the given values:
\[ A = \frac{(6 + 10) \times 8}{2} \]
Step 3: Perform the Calculation
Now, calculate the area:
\[ A = \frac{16 \times 8}{2} \]
\[ A = \frac{128}{2} \]
\[ A = 64 \]
Final Value
For a trapezium with bases \( a = 6 \) units, \( b = 10 \) units, and height \( h = 8 \) units, the area is \( 64 \) square units.
By following these steps, you can easily determine the area of a trapezium when the lengths of both bases and the height are given.
