  Lesson 5ª CALCULATING THE AREA OF A TRAPEZOID (trapezium)

A trapezoid (or trapezium) is a quadrilateral that has two parallel sides. A trapezoid is not a parallelogram. A parallelogram is a quadrilateral with two pairs of parallel sides.

In the images below, you have three types of trapezoids:
1) Rectangle trapezoids.- They have 2 right angles (90°) and 2 parallel sides.
2) Isosceles trapezoids.- The two sides which are NOT parallel have the same length.

3) Scalene trapezoids.- Its 4 sides have different lengths and it has 2 parallel sides. To calculate the area of a trapezoid, pay close attention to the four steps we will follow with a rectangle trapezoid:

First, draw a rectangle trapezoid.

Make a copy.

Turn the copy 180º.

Move the copy closer to the original.

Join them and you will get a rectangle whose base is the sum of the two bases.
Its height or width is still the same. Look at the steps in using the images below: If we calculate the area of the rectangle we have formed, we have: Is this the area of the trapezoid? NO,  because this rectangle was formed by two equal trapezoids. Now, the area of one of the trapezoids will be:  15(2).16    Draw two trapezoids that have a short base of 5 cm., a long base of 10 cm., and a height of 6 cm. Now, cut both trapezoids. Turn one of the trapezoids 180º and join them. Calculate the area of the rectangle you have formed and the area of one of the (equal) trapezoids:

Answers: 15(2).17   If instead of having used a rectangle trapezoid to calculate the area of a trapezoid, we would have used a scalene trapezoid, would the answer be the same?   Previous Lesson Next Lesson