Area Formula of Triangle

Foundational Knowledge

What is the area of the rectangle? What is the formula to find the area of a rectangle?

Right Triangles

There are two right triangles in the red rectangle above. A line has been plotted, so that the rectangle is split evenly into two equal, 90[math]^\circ[/math]triangles. How can we use what we already know about the area of rectangles to find the formula for the area of a right triangles? Think about the relationship between the shown triangle and the rectangles that it has been partitioned into.

Area of a Right Triangle

What is the base of one of the right triangles inside the red rectangle? What is the height of the same right triangles inside the red rectangle?

Calculate the area of a right triangle inside the red rectangle. Produce a rule that will help to find the area of a right triangle.

Triangle EFG

Using triangle EFG, I would like for you to test if your rule that you just created works in every situation to find the area of a triangle. Once you test and revise your formula, you are going to explore the variables of your formula independently and see how each one impacts the outcome (area).

Using triangle EFG, move the sliders and find the area of two different triangles? Show the math, using the formula you created for two different triangles.

If your formula is results in an area different from the one shown, then how can you revise your formula to make it correctly reflect the area of a triangle?

Triangle HIJ

Triangle HIJ has been split in half by a perpendicular bisector. Does the rule you created still reflect the area of half of the original triangle? Show your work.

Exploring Variables

Use the sliders of triangle EFG to see what happens when you double the base of the triangle. What was the impact that changing the base had on the area?

The area was cut in half. The area stayed the same. The area doubled that of the original area. The area was less than the original area.

Use the sliders of triangle EFG to see what happens when you double the height of the triangle. What was the impact that changing the height had on the area?

The area doubled that of the original area. The area stayed the same. The area was less than the original area. The area was cut in half.

What happens to area of the triangle when you double the base of the triangle, but the original triangle has been cut in half?

The area was less than the original area. The area stayed the same. The area was cut in half. The area doubled that of the original area.

Extension Triangle EFG

Write a function rule for the area of a triangle whose base is doubled that of its height?