Area of a Trapezium
In this activity you are going to explore the area of a trapezium, and how we can work out the area of any trapezium.
The orange point changes the height of the trapezium. The red points and blue points are the four vertices of the trapezium. Those of the same colour are on the same parallel line of the trapezium. The area of the parallelogram is given.
The orange point changes the height of the trapezium. The red points and blue points are the four vertices of the trapezium. Those of the same colour are on the same parallel line of the trapezium. The area of the parallelogram is given.
1) How will changing the height by moving the orange point affect the area of the trapezium?
Move the orange point to check your prediction. Were you correct?
How does the height of a trapezium affect the area?
Move the orange point to check your prediction. Were you correct?
How does the height of a trapezium affect the area?
2) What will happen to the area of the trapezium if you increase the base length by moving one of the red points?
Move one of the red points to check your prediction. Were you correct?
How is the base length of a trapezium related to the area?
Move one of the red points to check your prediction. Were you correct?
How is the base length of a trapezium related to the area?
3) How will moving one of the blue points affect the area of the trapezium?
Move one of the blue points to check your prediction. Were you correct?
Move one of the blue points to check your prediction. Were you correct?
Using all the information you have worked out, come up with a formula (in words or algebra) to calculate the area of any trapezium.
Ideas for Teachers
This activity is designed for students to use themselves to explore the area of trapezia. Getting them to investigate in the order above should slowly get them to see the links. It would make a good homework, for them to describe the process and thoughts they had in finding the formula.
You could also use this in front of a class, by asking them what they think will happen to the area before you move various points, then show them what happens. See if some of your students can spot which distances have an effect on the area.
This activity is designed for students to use themselves to explore the area of trapezia. Getting them to investigate in the order above should slowly get them to see the links. It would make a good homework, for them to describe the process and thoughts they had in finding the formula.
You could also use this in front of a class, by asking them what they think will happen to the area before you move various points, then show them what happens. See if some of your students can spot which distances have an effect on the area.
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