The perimeter of a 2D shape is the total distance around the boundary of the shape. For polygons (2D shapes made up of straight edges) we can find the perimeter by adding up the lengths of all the edges. This includes triangles, squares, rectangles, trapezia and other irregular polygons like the one below.
Perimeter $=16+12+4+8+8=48$=16+12+4+8+8=48 m
In practical problems we often encounter shapes that are combinations of sectors and polygons, as well as shapes with holes in them. These are known as composite shapes.
For these shapes we can find the perimeter by adding together all the lengths of the straight line segments and the arc lengths, remembering that if the shape has a hole in it then there is an internal boundary that also counts towards the perimeter.
We also encounter problems where not all of the side lengths are known. In many applications - such as surveying the dimensions of a block of land - taking length measurements can be time consuming, and so if we can work out some side lengths with a bit of thought, or by using formulas like Pythagoras' theorem, it will save time.
Practice questions
Question 1
Find the perimeter of the shape.
Question 2
Find the perimeter of the following figure correct to one decimal places.
Question 3
Ellie is fencing a paddock. The boundary is as shown in the diagram. The length across the paddock is $90$90 m.
Determine the length of the side labelled $x$x.
Round your answer to two decimal places.
What length of fencing does Ellie need?
Round your answer to two decimal places.
If the cost of the type of board she is using is $\$0.21$$0.21/m, how much will the fencing cost in total?
Round your answer to the nearest cent.