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How Do You Find the Perimeter and Area of a Trapezoid?


So far we have learned about the perimeter and area of a square, a rectangle, a rhombus and a parallelogram. Now we will look at how to find the perimeter and area of a trapezoid. But first, let’s take a look at one.

A trapezoid is a quadrilateral with two parallel sides of differing lengths. The other two sides can be at any length—and any angle!

Perimeter of a Trapezoid

To find the perimeter you need to add the length of all four sides. In a trapezoid, the four sides can, and usually are, all different lengths, so all four sides must be measured out and added together.

Perimeter of trapezoid

Formula

Perimeter of a Trapezoid

Two sides are parallel, but not the same length.

P = side1 + side2 + side3 + side4

Example 1

Find the perimeter of the following trapezoid:

Example of perimeter of trapezoid

You use the formula and add all four sides together: P = 2cm + 3cm + 3cm + 5cm = 13cm

Area of a Trapezoid

To find the area of a trapezoid you need to know the length of the two parallel sides and the height of the trapezoid. When you know this, you put the numbers into the following formula for the area of a trapezoid.

Area of trapezoid

Formula

Area of a Trapezoid

A = (a + b) h 2

The height is always a right angle to both the parallel sides. When you know the two lengths and the height, you can use the formula.

Example 2

Find the area of the trapezoid

Example of area of trapezoid

You find the area by using the formula: A = (4cm + 2cm) 3cm 2 = 6cm 3cm 2 = 18cm2 2 = 9cm2

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How Do You Find the Perimeter and Area of a Rhombus?