Understanding the Area and Perimeter of a Trapezium: Formulas and Examples

Trapezium, often referred to as a trapezoid in some regions, is a four-sided polygon with at least one pair of parallel sides. In this article, we will explore the formulas for calculating the area and perimeter of a trapezium, along with a few examples to make the concepts clearer.

Area of a Trapezium

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

A 12 × (b1 b2) × h

Where:

b1 length of the first base b2 length of the second base h height, the perpendicular distance between the two bases

Example

Consider a trapezium with bases b1 5 cm, b2 3 cm, height h 4 cm. We also know that the non-parallel sides are a 2 cm and c 2 cm.

Area:

A 12 × (5 3) × 4 12 × 8 × 4 16 cm2

Perimeter of a Trapezium

The perimeter P of a trapezium is the sum of the lengths of all its sides:

P a b1 b2 c

Where:

a length of one non-parallel side b1 length of the first base b2 length of the second base c length of the other non-parallel side

Example

Continuing with the same trapezium as in the area example, we have:

P 2 5 3 2 12 cm

Additional Calculations

For a trapezium with the formula simplified, the area can also be calculated as:

A 12 × (b a) × h

Where b and a are the lengths of the parallel sides.

Conclusion

If you have specific dimensions, feel free to share, and I can help you calculate the area and perimeter! Understanding these formulas can help you solve problems related to trapeziums in a straightforward manner.