what happens to the area of a triangle if its cut in half and double the base?

Question

what happens to the area of a triangle if the base gets doubled and the triangle is cut in half? And if the base is doubled without cutting it in half? what happens to the area in both instances, and why?

Answer 1

Hi Leslie,

The area will be the same as what you started with.
Doubling the base doubles the area.
Cutting the triangle in half cuts the area in half.

Why?

The formula for the area of a triangle will show you how to get this answer:
A = (1/2) * Base * Height
A = B/2 * H

If you double the base:
A = (B/2) * 2 * H
A = B * H (where B is the original base).
The area is doubled.

If you cut the triangle in half, the area is also cut in half.
I'm defining "cut in half" as cutting along a line from any vertex to the midpoint of the opposite side of the triangle. If you consider that opposite side to be the base, this cut will cut the base in half without changing the height. Just the opposite of doubling the base.

It doesn't matter which way you cut the triangle in half:
Draw a triangle, identify the base and height. Then draw the dividing line that bisects that base. The base is cut in half and the height is still the same.
Now look at it again using a different side as the base. The shape might be different using the different base, but the area will still be cut in half.

I hope this helps!