A trapezoid (or trapezium in some countries) is a four-sided figure with at least one pair of parallel sides, referred to as the ‘bases’ of the trapezoid. The area of a trapezoid can be calculated using a specific formula, which is useful in geometry, architecture, and various engineering fields.
Trapezoid Area Formula
The area of a trapezoid is given by the formula: Area = (1/2) × (sum of the lengths of the two parallel sides) × (height). In notation, this is expressed as A = 1/2 (a + b) h, where ‘a’ and ‘b’ are the lengths of the parallel sides, and ‘h’ is the height (the perpendicular distance between the parallel sides).
How to Use the Trapezoid Area Formula
- Measure the lengths of the two parallel sides of the trapezoid.
- Measure the height (the perpendicular distance) between these parallel sides.
- Substitute these values into the formula and calculate the area.
Examples of Calculating Trapezoid Area
Example 1: A trapezoid has parallel sides of lengths 6 cm and 4 cm, and the height is 5 cm. Its area is 1/2 (6 + 4) × 5 = 1/2 × 10 × 5 = 25 cm².
Example 2: For a trapezoid with parallel sides measuring 10 m and 7 m, and a height of 3 m, the area is 1/2 (10 + 7) × 3 = 1/2 × 17 × 3 = 25.5 m².
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