Geometry: The Basics

Two words come up over and over. Perimeter is the distance all the way around the outside of a shape, like a fence around a yard. Area is how much flat space is inside, like carpet on a floor.

The formulas are short. Rectangle area is length times width. Square area is side times side. Triangle area is one half times base times height. Perimeter is always just adding up every side.

Angles follow four facts. A straight line is $180°$. A right angle is $90°$. The three angles in any triangle add to $180°$. And when two lines cross, the angles directly across from each other are equal.

For right triangles, use $a^{2} + b^{2} = c^{2}$, where $c$ is the hypotenuse — the long side across from the right angle. The sets 3-4-5, 6-8-10, and 5-12-13 show up constantly.