Finding the Height of a Trapezium: A Comprehensive Guide

Understanding the geometry of shapes, particularly calculating the height of a trapezium, is an essential skill in many fields, including mathematics, engineering, and architecture. This article will guide you through the process of finding the height of a trapezium using the formula for its area.

The Formula for the Area of a Trapezium

The area of a trapezium (also known as a trapezoid) can be calculated using the formula:

Area frac12; × (sum of parallel sides) × height.

Step-by-Step Solution

Let's consider a trapezium where the lengths of the parallel sides are 12 cm and 8 cm, and its area is 60 square cm. We want to find the height of this trapezium.

The formula for the area of the trapezium is: Area frac12; × (a b) × h Substitute the given values into the formula: 60 frac12; × (12 8) × h Calculate the sum of the parallel sides: 12 8 20 Substitute back into the equation: 60 frac12; × 20 × h This simplifies to: 60 10 × h Now solve for h: h frac6010 6 text{ cm}

Therefore, the height of the trapezium is 6 cm.

Additional Examples and Calculations

Here are a few more examples to further illustrate the calculation process:

Example 1:

Given: Area 80 cm2, a 9 cm, b 7 cm. Area formula for a trapezium: Area frac{a b}{2} × height Substitute the values: 80 frac{9 7}{2} × height Calculate the sum of the parallel sides: 9 7 16 Substitute back into the equation: 80 frac{16}{2} × height This simplifies to: height frac{80}{8} 10 text{ cm}

Example 2:

Given: Area 80 cm2, a 9 cm, b 7 cm. Area formula for a trapezium: Area frac{a × b}{2} × height Substitute the values: 80 frac{9 × 7}{2} × height This simplifies to: 80 frac{63}{2} × height Isolate height: height frac{80}{frac{63}{2}} frac{160}{63} approx 2.54 text{ cm}

These examples demonstrate the versatility and application of the trapezium area formula in solving for dimensions.

Conclusion

By following the above steps and utilizing the area formula for a trapezium, you can easily find the height of a trapezium given its area and the lengths of its parallel sides. Whether for educational purposes or professional work, mastering this calculation ensures accuracy and efficiency in geometric problem-solving.