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Video

What is Perimeter?

Perimeter is the distance around the outside of a shape. For example, if you walk the distance around the edge of a playground, you are walking its perimeter.

Lets explore how we can calculate the perimeter of these shapes:

  • Triangles
  • Rectangles
  • Regular Polygons
  • Circles

perimeter pi

Units

We write perimeter in the units we use to measure the shape. For example, if we measure in centimeters, we write the answer in centimeters. If we measure in miles, we write the answer in miles.


Triangles

If we look at a triangle, we can see it is made up of three sides. Adding the length of the sides tells us the perimeter of the shape.

  • Perimeter = 3 + 4 + 5
  • Perimeter = 12 feet
perimeter triangles

Rectangles

In a rectangle the opposite sides have equal lengths. If we add all four of the sides together we can calculate the perimeter.

  • Perimeter = 8 + 8 + 6 + 6
  • Perimeter = 28 feet
perimeter rectangles

We can also calculate the perimeter of a rectangle using a formula:

  • Perimeter = 2 × (Width + Height)
  • Perimeter = 2 × (8 + 6)
  • Perimeter = 2 × 14
  • Perimeter = 28 feet

Regular Polygons

Some shapes have lots of sides. We call them polygons. ‘Poly’ means ‘many’. Triangles, rectangles, pentagons, hexagons are all examples of polygons

A regular polygon has sides that are all the same length (congruent). A regular pentagon has five sides. We can calculate the perimeter of regular polygons by multiplying the number of sides by the length of one side.

  • Perimeter = Number of Sides × Length of One Side
  • Perimeter = 5 × 4
  • Perimeter = 20 yards
perimeter formula

Hatch Marks

There is a special symbol made up of small parallel lines called hatch marks. Where these hatch marks match, the sides have the same length.

  • Perimeter = 8 + 8 + 4 + 4
  • Perimeter = 24 feet
perimeter hatch marks

Complex Shapes

We can even find the perimeter of complex shapes, like this one. We simply need to add up the measurements of each side of the shape.

  • Perimeter = 10 + 2.5 + 5 + 2.5 + 5 + 5
  • Perimeter = 30 cm
perimeter complex shapes

Circles

Finding the perimeter of a circle can be tricky! We need to remember that a circle is still a two dimensional shape with an outside edge that we can measure. We know that a circle only has one edge – all around the outside. We use a special word for the perimeter of a circle – it is called the circumference.

We can use a formula to help us find the circumference of a circle. We need the radius of the circle and π (Pi) which is a special number equal to 3.14 (rounded). The radius is the length from the center of the circle directly to the outside edge. The formula we need to use is 2 × Radius × π (Pi) (More information on Pi below).

  • Circumference = 2 × Radius × π
  • Circumference = 2 × 5 × 3.14
  • Circumference = 31.4 cm
perimeter circles

Pi

Did you know π (Pi) is the circumference of a circle divided by its diameter? So another way to calculate the circumference (perimeter) of a circle is multiply the diameter by π. A circle’s circumference is always roughly three times the circle’s diameter.

  • π = Circumference/Diameter
  • π = 3.14 (Rounded)
  • Circumference = Diameter × Circumference/Diameter
  • Circumference = Diameter × π
  • Circumference = Diameter × 3.14
  • Circumference = 10 × 3.14
  • Circumference = 31.4 cm
perimeter pi

Using Perimeter in Real Life

There are many situations where perimeter is useful in real life.

  • Measuring the radius of a bike wheel for a new tire.
  • Planning a run around the perimeter of a local park.
  • Making a garden border.
  • Fencing a yard.
  • Building a sandbox.
  • Planning for new kitchen cabinets.

Activity

Here’s a great way we can explore the concept of perimeter:

Find some common household objects of various sizes – look for things which have a two dimensional flat surface that can be easily measured. Things like a a book, a plate, or a slice of bread are all great to use.

perimeter activity

Here’s what to do:

  1. Find a piece of string that is longer than the outside of the object.
  2. Wrap it all the way around so that it overlaps itself.
  3. Mark this point with a marker.
  4. Lay the string out flat next to a ruler or tape measure.
  5. Measure from the start of the string to the point marked.
  6. This measurement is the perimeter of the object.