Triangle and Parallelogram Families
What is a Triangle Family?
A triangle family is a group of triangles with the same base and height.
As you see in this picture, all of these triangles have the same base of 4cm and a height of 7cm. However, the perimeter changes and the area stays the same. The area stays the same because you are still using the same base and height. The formula for finding the area of a triangle is A =1/2 bh. You can make an infinite amount of triangles with the same base and height.
What is a Parallelogram Family?
A parallelogram family is a group of parallelograms with the same base and height.
In the picture above, you see that the base and height of these parallelograms stay the same but, the perimeter changes. The area of the parallelograms are the same because the formula for finding the area of parallelograms is A =bh. When you have a parallelogram family the height and base remain the same but the side lengths change which affect the perimeter. You can make an infinite amount of parallelograms with the same base and height.
Why does the area stay the same and the perimeter changes?
When finding the area of a parallelogram you do not use the side lengths only the base and height matter. The same is true for finding the area of a triangle. That is why the area remains the same in a family of parallelograms or triangles. The perimeter changes because the side lengths change.
Blog Post Written By: EO & SR