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The area of a convex polygon is the space filled by its surface. Every time we obtain the calculation of the area of a certain region, its measurement unit will be squared (km², cm², m² etc.).

O **trapeze** it is a quadrilateral, given that it has four sides. The sum of its internal and external angles equals 360°. Every trapeze has a pair of parallel sides. Look at the figure below:

To calculate the area of a trapezoid, we must know the measurements referring to the major base (b), minor base (a) and height (h). Look:

**♦ Trapezium area formula**

The formula we use to calculate the trapeze area is as follows:

**A = ½. h (a + b)**

A = Trapezium area.

h = height.

a = base smaller.

b = larger base

Let's solve two examples to learn how to use the trapeze area formula.

**♦ Trapezium area calculation examples**

**Example 1**

Calculate the area of the trapeze below:

A = ½. H. (a + b)

A = ½. 8. (5 + 15)

A = ½. 8. (20)

A = ½. 160

A = 160/2

H = 80 m^{2}

**Example 2**

The trapeze is one of the polygons used in making mosaics.

Suppose that one of the red tiles in the mosaic has the following measurements: Larger base: 4 cm, smaller base 2 cm, and 2.5 cm height. Calculate the area of this piece of the mosaic.

b = 4 cm

a = 2 cm

h = 2.5 cm

A = ½. H. (a + b)

A = ½. 2.5 cm. (4 cm + 2 cm)

A = ½. 2.5 cm. (6 cm)

A = ½. 15 cm^{2}

A = __15 cm__^{2}

2

H = 7.5 cm^{2}

By Naysa Oliveira

Graduated in Mathematics

**Source:** Brazil School - https://brasilescola.uol.com.br/matematica/area-trapezio.htm