Area of Trapezoid Formula, Definition, Solved Examples

Area of Trapezoid Formula: In Geometry, a trapezoid belongs to the category of quadrilaterals characterized by having a set of parallel sides (referred to as bases) and another set of non-parallel sides (referred to as legs). The area of a trapezoid represents the count of unit squares that can be accommodated within its shape. Typically, this measurement is expressed in square units like cm², m². This discussion aims to discuss  the detailed understanding of the trapezoid's area formula and its application through examples.

Area of Trapezoid Formula

The calculation for the area of a trapezoid involves knowing the lengths of its parallel sides (denoted as "a" and "b") and the perpendicular distance between these sides ("h").

Expressed as:

Area of a Trapezoid = (½) [(a + b)h] square units.

Area of Trapezoid Formula Solved Examples

Example 1: Determine the area of a trapezoid with bases measuring 6 cm and 7 cm and a perpendicular distance of 8 cm between them.

Solution:

Given:

Let the parallel sides of the trapezium be denoted as “a” and “b”.

Thus, a = 6 cm and b = 7 cm.

Additionally, the perpendicular distance between the parallel sides is stated as 8 cm (i.e., h = 8 cm).

The area of  trapezoid formula is: A = (½) [(a + b)h] square units

Now, putting the values into the formula:

A = (½) [(6 + 7)8] square units

A = 13 * 4 cm²

A = 52 cm²

Hence, the area of the trapezoid is 52 cm².

Example 2: Calculate the height of the trapezoid if the sum of the parallel sides is 25 m and the area measures 75 m².

Solution:

Given: a + b = 25 m

Area, A = 75 m²

To find: h

Utilizing the formula for the area of a trapezoid, A = (½) [(a + b)h] square units

Putting the provided values into the formula:

75 = (½) * 25h

75 / 25 = (½)h

3 = h / 2

h = 6

Therefore, the height of the trapezoid is 6 meters.

Example 3: Given a trapezoid with bases measuring 10 inches and 14 inches, and a height of 6 inches. Calculate the area of the trapezoid.

Solution:

Given:

Base lengths: a = 10 inches, b = 14 inches

Height: h = 6 inches

Using the formula for the area of a trapezoid: A = (½) [(a + b)h] square units

Substituting the given values:

A = (½) [(10 + 14)6] square units

A = (½) * 24 * 6

A = 72 square inches

Therefore, the area of the trapezoid is 72 square inches.

Example 4: If the lengths of the parallel sides of a trapezoid are 12 meters and 18 meters, with a height of 9 meters, determine its area.

Solution:

Given:

Let the parallel sides of the trapezoid be denoted as “a” and “b”.

Thus, a = 12 meters and b = 18 meters.

The height, which is the perpendicular distance between the parallel sides, is 9 meters (i.e., h = 9 meters).

The formula for the area of a trapezoid is: A = (½) [(a + b)h] square units.

Now, substituting the provided values into the formula:

A = (½) [(12 + 18)9] square units.

A = (½) * 30 * 9 square meters.

A = 135 square meters.

Therefore, the area of the trapezoid is 135 square meters.

Understanding the area of a trapezoid involves recognizing the essential elements: its two parallel sides (bases) and the perpendicular distance between them. The formula, Area of a Trapezoid = (½) [(a + b)h] square units. serves as a fundamental concept in calculating the space enclosed within this geometric shape.

The formula for the area of a trapezoid provides a simple yet effective method to compute the enclosed space within this four-sided figure, facilitating applications across mathematics, engineering, construction, and other fields requiring geometric calculations.

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