Google Classroom
GeoGebraGeoGebra Classroom

Area of Trapezia

Introduction

In the following activity, you will work through and explain 3 methods for finding the areas of a trapezium. There is a formula, but it is best to see where it comes from.
Approach 1

In the applet above, Step 0 shows a trapezium. Step 1 allows you to rotate a copy of the trapezium by a given angle (from 0 to 180°). What do you notice about the shape formed when the angle is 180°? Has it got a special type?

How would you find the area of the shape you identified in the previous question? What is the area of this shape?

Can we use this to find the area of the original trapezium? How?

What is the area of the trapezium?

Select all that apply
  • A
  • B
  • C
  • D
  • E
Approach 2

In the applet above, Step 0 shows a trapezium. Step 1 also allows you to rotate by a given angle (from 0 to 180°). What do you notice about the shape formed when the angle is 180°? Has it got a special type?

How would you find the area of the shape you identified in the previous question? What is the area of this shape?

Can we use this to find the area of the original trapezium? How?

What is the area of the trapezium?

Select all that apply
  • A
  • B
  • C
  • D
  • E
Approach 3

In the applet above, Step 0 shows a trapezium. Step 1 allows use of another slider. What does this slider do?

For either option, how could you find the area of the trapezium?

What is the area of the trapezium?

Select all that apply
  • A
  • B
  • C
  • D
  • E