Rectangles, triangles, and polygons

For any shape with straight sides, the perimeter formula is always the same idea: add up every side. Each formula below is just a shortcut for that sum.

Rectangle: 2(w + h)

A rectangle has two widths and two heights — opposite sides are equal. So instead of adding all four, double the pair:

P = 2(w + h)

A 9 × 4 rectangle: P = 2(9 + 4) = 2 × 13 = 26 units.

The shortcut saves a step, but it's still just the four sides added together.

Triangle: a + b + c

A triangle has three sides, and they're all different unless it's a special case. There's no shorter formula — just name the sides and add:

P = a + b + c

A triangle with sides 5, 12, and 13: P = 5 + 12 + 13 = 30 units.

(That happens to be a right triangle — check: 5² + 12² = 169 = 13².)

Regular polygon: n × s

A regular polygon has n equal sides, each of length s. So the perimeter is just n copies of the same side:

P = n × s

A regular hexagon (6 sides) with s = 7: P = 6 × 7 = 42 units.

This is exactly what makes regular polygons easy: one side length tells you everything.

The pattern behind all three

All straight-sided perimeters share one rule: count every side once and add. The shortcuts (2(w+h), n×s) only work because they exploit symmetry — equal sides pair up. When the sides aren't equal, just list them and sum.