Angles and PolygonsPerimeter and Area

The perimeter of a polygon is the total distance around the outside — it is the sum of all its side lengths.

Move the vertices of this polygon and watch the perimeter change:

Perimeter = ${perim} units

For a regular polygon, the perimeter is easy to calculate. Since all sides are equal:

Perimeter = number of sides × side length

A regular hexagon with side length 5 cm has a perimeter of × = cm.

The area of a polygon is the amount of space it covers. We measure area in square units (like cm² or m²).

The simplest polygon to find the area of is a rectangle:

Area of a rectangle = length × width

A rectangle that is 8 cm long and 5 cm wide has an area of × = cm².

We can find the area of a triangle by thinking of it as half a rectangle:

A triangle with base 10 cm and height 6 cm has an area of ½ × × = cm².

For any polygon, we can find its area by splitting it into triangles and rectangles. This is called decomposition.

We draw diagonals to split the polygon into triangles, then add up the areas of all the triangles. This method works for any polygon!