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.