Finding the area of ​​a trapezoid: formula and examples

Trapezium is a geometric figure; a quadrilateral with 2 parallel and 2 non-parallel sides.

Area formulas

By base length and height

The area of ​​the trapezoid (S) equals half the sum of its bases multiplied by the height drawn to them.

Through the lengths of all sides (Heron’s formula)

To calculate the area of ​​a trapezoid, you need to know the lengths of all its sides:

p – semiperimeter of a trapezoid, calculated by the formula:

Through the diagonals and the angle between them

The area of ​​a trapezoid is half the product of the diagonals and the sine of the angle between them. Calculated using one of the two formulas below:

Examples of tasks

Task 1

Find the area of ​​a trapezoid if its bases are 4 and 7 cm and its height is 4 cm.

Decision:

We use the first formula discussed above: S = ¹/₂ *(4cm+7cm)*4cm=22cm².

Task 2

Find the area of ​​a trapezoid if its bases are 6cm and 12cm and its sides are 8cm and 10cm.

Decision:

Because we know the lengths of all sides, we apply Heron’s formula:

S = (6+12) / |6-12| * √(18-6)(18-12)(18-6-8)(18-6-10) = 18 / 6 * √576 = 72 cm².