EXPERIMENTING WITH AREA AND PERIMETER: TRIANGLES
Introduction and Background
Looking at a collection of different polygons, there are two ways to decide which is the “largest” or which is the “smallest.”
One way to decide is to measure the area of each using unit squares, and then compare.
Another way to decide is to measure the length of the perimeter of each, then decide.
Step 1. Make Observations
Use the MOVE (pointer) tool to drag the blue corner points of the triangles to change the shape of the triangles. Watch the area and perimeter labels as they change. Experiment with several triangles.
Step 2. Construction Problems
1. Construct a red triangle that is larger in area than the blue triangle, but is smaller in perimeter.
Area Red = ______ square units Perimeter Red = _______ units of length
Area Blue = ______ square units Perimeter Blue = _______ units of length
2. Construct a red triangle that is smaller in area than the blue triangle, but is larger in perimeter.
Area Red = ______ square units Perimeter Red = _______ units of length
Area Blue = ______ square units Perimeter Blue = _______ units of length
3. Construct a red triangle and a blue triangle that both have an area of 25 square units, but look completely different from each other.
Mathematicians would say that these two triangles are not similar. Sketch your two triangles:
4. Construct a red triangle and a blue triangle that both have a perimeter of 20 units, but look completely different from each other – are not similar. Sketch your two triangles:
5. Now a more challenging problem: Construct a red triangle and a blue triangle that have the same area and the same perimeter, but look completely different from each other – are not similar. Sketch your two triangles: