the height of a triangle with vertices (1,5) (2,3) and (-1,-6) is multiplied by 4 what is the change in the area?

Answer 1

This problem looks more complicated than it is. You are given information about a specific triangle (the vertices). However, the answer to the question "What happens to the area of a triangle when the height of a triangle is multiplied by 4?" is the same for all triangles. We can ignore the vertices and think algebraically about the area formula, which, I think, makes the problem more straight forward.

So, what happens to the area of a triangle when you multiply its height by 4?

The area of a triangle formula is 1/2 * Base * Height = Area.

Now lets multiply the height by 4: 1/2 * Base * Height *4 = New Area

What is different between the original area and the new area? *4 (The original area formula is bolded in the new area formula) Since we changed nothing else (base, height), the new area is four times the original area.

This will be true for any triangle. So, the answer to the original question is: the new area will be four times the old area. If you are skeptical, pick a few random numbers for base and height and try it. If you multiply the height by four, is your area four times the original area?