Why is the area of a triangle (Base × Height) ÷ 2? When students just memorize the formula, they often forget the ÷ 2 part. But when they see the geometric connection between triangles and rectangles, they never forget it.

The Paper Rectangle Experiment

  1. Take a regular rectangular index card. Its area is Base × Height.
  2. Draw a diagonal line from one corner to the opposite corner.
  3. Cut along the line with scissors.
  4. What do you have? Two identical right triangles!

Since the two triangles make up the exact same rectangle, one triangle MUST have half the area: (Base × Height) ÷ 2.

What About Non-Right Triangles?

Even acute or obtuse triangles can be split into two right triangles or enclosed in a rectangle. In every case, the triangle covers exactly 50% of the enclosing rectangle's area.