Class VI

Shapes and fractions - perimeter

Lesson

Perimeter of shapes

We have seen how we can calculate the perimeter of a two dimensional shape, by adding up the length of each side of the shape. We can also talk about perimeter in terms of fractions. Fractions are parts of a whole, so we can think of part of the perimeter of our shape as a fraction of the total perimeter.

What if the denominator is different to the number of sides?

What if we have a shape with $5$5 sides, but we need to walk $\frac{1}{6}$16 of the perimeter? We can't walk one side of our shape, since this would only be$\frac{1}{5}$15, so we need a strategy to find out where $\frac{1}{6}$16 places us.

You could use equivalent fractions to help you, or you could use the strategy we use in Video 2. By comparing $\frac{1}{6}$16 to $\frac{1}{5}$15 (the point we do know), we can work out if our point is before, or after this point.

Remember!

We can only use fractions to calculate perimeter this way if our shapes have sides of equal length.

Worked examples

Question 1

Consider the square below:

If you start at point $A$A and travel clockwise $\frac{1}{2}$12 of the way around the square, where do you end up?

End point $=$= $\editable{}$
If you start at point $A$A and travel clockwise $\frac{1}{4}$14 of the way around the square, where do you end up?

End point $=$= $\editable{}$

Question 2

Consider the equilateral triangle below:

If you start at point $A$A and travel clockwise until you reach point $C$C, what fraction of the triangle have you travelled along?

Fraction $=$= $\frac{\editable{}}{\editable{}}$
If you start at point $A$A and travel clockwise until you reach point $G$G instead, what fraction of the triangle have you travelled along?

Fraction $=$= $\frac{\editable{}}{\editable{}}$

Question 3

Consider the pentagon below, which has five sides of equal length:

If you start at point $A$A and travel clockwise $\frac{1}{4}$14 of the way around the pentagon, where do you end up?

End point $=$= $\editable{}$
If you start at point $A$A and instead travel clockwise $\frac{3}{4}$34 of the way around the pentagon, where do you end up?

End point $=$= $\editable{}$

Outcomes

6.G.CPA.1

Introduction and general understanding of perimeter using many shapes. Shapes of different kinds with the same perimeter. Concept of area, Area of a rectangle and a square Counter examples to different misconceptions related to perimeter and area.