Perimeter and Area
Perimeter and area get mixed up constantly, and the reason is that both get called "the size of the shape". They measure different things: one is the walk around the edge, the other is the space inside. This track keeps them apart by building area out of counting rather than formulas — fit squares inside a rectangle and length × width turns out to be a shortcut for counting them, not a rule to memorise. A square is that same grid needing only one measurement. A triangle is exactly half of the rectangle that boxes it in, which you can see rather than take on trust. The circle comes last because it has no sides to count and its area has to be discovered instead: every circle holds a little over three squares built on its own radius, which is where pi comes from.
CodePLU Goal
Upgrading Human Mental Models
Learn how to think in Workflows
What Is Perimeter, and How Do You Find It?
Perimeter is the distance around the outside of a shape — the fence, not the grass. It is measured in lengths rather than squares, which is the whole of what separates it from area. Walk six shapes round the edge and match each to its perimeter on a grid.
How Do You Find the Area of a Rectangle?
Area is not a formula to remember — it is a count of the squares that fit inside a shape. Once you can see the squares, length × width stops being a rule and becomes the fastest way to count rows. Match each multiplication to the rectangle it describes in an interactive playground.
How Do You Find the Area of a Square?
A square is a rectangle whose sides happen to match, so its area is still a count of the squares inside it — you just only need to measure once. That is why it is written s², and why area and square numbers are the same idea. Pick the real squares out of a grid in an interactive playground.
How Do You Find the Area of a Triangle?
Every triangle fits inside a rectangle and fills exactly half of it. That single fact is where the half-base-times-height formula comes from, and seeing it means you never have to trust the formula again. Match each triangle to its area on an interactive grid.
How Do You Find the Area of a Circle?
A circle has no rows of squares to count, so its area is measured against a square built on its own radius. It always holds a little over three of them, and that little-over-three is pi. Match each circle to its area on an interactive grid.