Our goal over the next several activities will be to find an area formula for triangles. In order to do this, we need to start by identifying the base and height for triangles.

On the triangle below, draw the height of the triangle in three different ways.
(a)
Use side as the base.
(b)
Use side as the base.
(c)
Use side as the base.

The first type of triangles we will work with are right triangles.

Use a moving and additivity strategy to find a formula for the area of the triangle below in terms of , the length of its base, and , the length of its height. If you move and reattach pieces of the triangle or make copies of the triangle, you should prove that they fit exactly as you claim.
Use a different moving and additivity strategy than you did in the first problem to find a formula for the area of the triangle below in terms of , the length of its base, and , the length of its height. If you move and reattach pieces of the triangle or make copies of the triangle, you should prove that they fit exactly as you claim.
Use a third different moving and additivity strategy to find a formula for the area of the triangle below in terms of , the length of its base, and , the length of its height. If you move and reattach pieces of the triangle or make copies of the triangle, you should prove that they fit exactly as you claim.
2025-09-14 02:54:07