Area Formulas

Pre-Algebra · Axiom Academy

LESSON Area Formulas, Cut Apart Why is a triangle's area base times height over two? Cut the shapes apart and watch every formula fall out of the rectangle. 1. Rectangle: Counting Squares Area measures how many unit squares fit inside a shape. Take a rectangle 5 units wide and 3 units tall. We could fill it square by square and count to 15 — but the squares land in a neat grid, so a faster route is to multiply the rows by the columns. 3 rows of 5 squares = 15 squares 2. Parallelogram: Slide It Into a Rectangle A parallelogram looks tilted, but watch what happens when we slice the slanted triangle off one end and slide it over to the other end. Nothing is added and nothing is thrown away — the leaning shape stands up into a perfect rectangle . same base, same height, same area as the rectangle 3. Triangle: Half of a Parallelogram Here is the trick for triangles. Make an identical copy , spin it halfway around, and dock it against the original. The two copies lock together into a parallelogram — one whose base and height match the triangle's. one triangle is exactly half the parallelogram Step back and the whole family lines up. Everything starts at the rectangle; each new formula is the one before it after a single cut-and-rearrange move. Watch the same shape morph down the chain. Rectangle — (count the unit squares). Parallelogram — (slide the end to make a rectangle). Triangle — (it is half a parallelogram).

This is the written version of the interactive lesson above. See the full Pre-Algebra course.