How to Calculate the Distance Between Parallel Sides of a Trapezium Using Its Area

Calculating the distance between the parallel sides (height) of a trapezium can be a straightforward process if you know the area and the lengths of the parallel sides. This article will walk you through the steps to find the height of a trapezium given its area and the lengths of the parallel sides, in this case, 30 cm and 14 cm with an area of 440 cm2.

Understanding the Trapezium Area Formula

The area (A) of a trapezium can be calculated using the formula:

Formula:
A 1/2 × (a b) × h

Where:

A is the area of the trapezium a and b are the lengths of the parallel sides (bases) h is the height, or the distance between the parallel sides

Given Values and Step-by-Step Solution

Given:

Area (A) 440 cm2 a 30 cm b 14 cm

To find the height (h), we substitute the given values into the formula:

A 1/2 × (a b) × h

Substitute the values:

440 1/2 × (30 14) × h

Calculate 30 14:

440 1/2 × 44 × h

This simplifies to:

440 22h

Solve for h:

h 440 / 22

h 20 cm

Thus, the distance between the parallel sides is 20 cm.

Alternative Methods to Verify the Calculation

There are a few alternative methods to verify the calculation of the height of the trapezium:

Area 1/2 × (a b) × h 720 1/2 × (13 7) × h

A 1/2 × (713) × h 720

720 10h

h 72 cm

A 1/2 × (a b) × h 720 1/2 × (13 7) × h

A 1/2 × (30 14) × h 720

720 10h

h 72 cm

Let the distance between the parallel sides be d cm. A 1/2 × (713) × d

720 1/2 × 10 × d

720 10d

d 72 cm

Conclusion

The distance between the parallel sides of the trapezium is 20 cm. This calculation is based on the area formula of a trapezium, which is 1/2 × (a b) × h. By substituting the given values and solving for h, you can find the distance between the parallel sides.

For further exploration, you can try calculating the distance between parallel sides with different areas and lengths of bases, or explore the other alternative methods mentioned. Understanding these calculations and formulas can be useful in various fields, including geometry and architecture.