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4.08 Perimeter of land



The perimeter of a plot of land is the total length of the boundary.  Perimeter can be thought of as the length of a fence that would fully separate the plot from other pieces of land.

We can work out the perimeter by adding the lengths of the pieces that make up the boundary. This assumes that someone, possibly a surveyor, has done the measurements and has made them available.

However, sometimes certain measurements have been carried out but not all of the boundary lengths are known until further calculations, perhaps using Pythagoras' theorem, are carried out.

Sometimes it may be necessary to use an accurate scale diagram of the plot of land to recover missing measurements. This can be done by measuring distances on the diagram and using a scale factor to find the real length. A scale diagram might also be drawn on a grid that shows unit lengths. These can be used to read the total length directly from the diagram.

Diagrams of plots of land can include measurements other than the required boundary measurements. If so, one must be careful to include only the relevant measurements in the perimeter calculation.


Worked example

In this diagram of a plot of land, the measurements of all of the boundary segments have been given. To calculate the perimeter, all that is needed is to add the five boundary measurements.

$\text{perimeter}=22.4+11.6+34.6+2.9+16.0=87.5$perimeter=22.4+11.6+34.6+2.9+16.0=87.5 m


Scale drawings

Think of a line segment representing a piece of the boundary of some land. Suppose the line, on paper, is $3.5$3.5 cm long.

There is a scale included with the drawing that tells us that $1$1 cm on the drawing represents $2.5$2.5 m on the ground. This means that the $3.5$3.5 cm line would be equivalent to $3.5\times2.5=8.75$3.5×2.5=8.75 m on the ground.

To make use of this technique, you may need to physically measure the distances in a scale drawing with a ruler before multiplying each measurement by the scale factor.


Practice questions

Question 1

An outline of a block of land is pictured below.

  1. Find the length of the side labelled $x$x m.

  2. Find the perimeter of the block of land in metres.

Question 2

In the following diagram, each square of the grid has a side length of $30$30 m. A jogger runs the perimeter of the park $4$4 times each morning.

  1. What is the distance of one lap of the park?

  2. How far will the jogger run each week? Give your answer in kilometres.

Question 3

Consider the following section of a street map.

  1. We want to calculate the perimeter of the block of land occupied by 15 Algebra Road and 150-152 Rhombus Road. Which diagram provides the most reasonable estimate for the lengths of the sides based on the scale provided?




  2. Hence, calculate the perimeter of the block of land in metres.



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