Understanding the Area of a Trapezium: Formulas and Examples
A trapezium, also known as a trapezoid, is a fascinating geometric shape with unique properties. It is characterized by having at least one pair of parallel sides. Calculating the area of a trapezium can be done using different formulas, depending on the given measurements. In this article, we will explore the area of a trapezium with particular emphasis on the formula and provide examples to illustrate the concept.
The Formula for Calculating the Area of a Trapezium
The area A of a trapezium can be calculated using a specific formula, which involves the lengths of the parallel sides and the height (perpendicular distance between the parallel sides). The formula is as follows:
A frac{1}{2} times (b_1 b_2) times hwhere:
b_1 and b_2 are the lengths of the parallel sides. h is the height, which is the perpendicular distance between the parallel sides.Example 1: Calculating the Area of a Trapezium
Consider a trapezium with the lengths of the parallel sides as 10 cm and 6 cm, and the perpendicular distance between these sides is 4 cm.
Identify the given values:b_1 10 , text{cm}
b_2 6 , text{cm}
h 4 , text{cm}
Substitute these values into the formula:A frac{1}{2} times (10 6) times 4
Simplify the expression:A frac{1}{2} times 16 times 4
A 8 times 4 32 , text{cm}^2
The area of this trapezium is 32 cm2.
Example 2: Another Trapezium Area Calculation
Let's consider another trapezium with a base 1 and base 2 as 8 cm and 4 cm, respectively, with a height (perpendicular distance between the sides) of 5 cm.
Identify the given values:b_1 8 , text{cm}
b_2 4 , text{cm}
h 5 , text{cm}
Substitute these values into the formula:A frac{1}{2} times (8 4) times 5
Simplify the expression:A frac{1}{2} times 12 times 5
A 6 times 5 30 , text{cm}^2
The area of this trapezium is 30 cm2.
Conclusion
Calculating the area of a trapezium is straightforward once you understand the formula ((b_1 b_2)/2 times h). This formula is derived from the area of a parallelogram, where the trapezium essentially behaves like a half-parallelogram between the parallel sides. By applying this formula, you can easily find the area for any trapezium given the lengths of its parallel sides and the height between them.