The perimeter of a polygon is the combined length of all its straight-line sides. We can use the properties of simple polygons like triangles or rectangles to find the perimeter of irregular polygons, as in this example.

## Problem

Find the perimeter of the following shape, created by cutting a triangle from a square with side 5 units, as in the following drawing.

## Strategy

The original shape was a square, so the three sides that remain of the square are all equal and measure 5 units each.

The hint for finding out the two other sides is in the angle – 30 °. The original angle of the square was 90°, so if we draw the missing side =of the square, we’ll have a triangle with two angles measuring 60°.

So it must be an equilateral triangle, whose sides all equal 5 (the length of the missing side of the square, which is also a side of the equilateral triangle).

So the perimeter is 5+5+5+5+5=25 units.