Area of a Triangle
In this activity you are going to explore the area of a triangle, and how we can work out the area of any triangle.
Use the orange point to change the height of the triangle. Move the blue point to change the type of triangle. Move the red point to change the base length of the triangle. The area is given for each triangle you make.
Use the orange point to change the height of the triangle. Move the blue point to change the type of triangle. Move the red point to change the base length of the triangle. The area is given for each triangle you make.
1) If you were to move the blue point one square to the left, what would the area of the new triangle be?
Now move the blue point to check your prediction. Were you correct?
What does this tell us about triangles with the same height and base length?
Now move the blue point to check your prediction. Were you correct?
What does this tell us about triangles with the same height and base length?
2) What will happen to the area of the triangle 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 triangle related to the area?
Move one of the red points to check your prediction. Were you correct?
How is the base length of a triangle related to the area?
3) How will changing the height by moving the orange point affect the area of the triangle?
Move the orange point to check your prediction. Were you correct?
How does the height of a triangle affect the area?
Move the orange point to check your prediction. Were you correct?
How does the height of a triangle affect the area?
Using all the information you have worked out, come up with a formula (in words or algebra) to calculate the area of any triangle.
Ideas for Teachers
This activity is designed for students to use themselves to explore the area of triangles. 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 triangles. 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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