Download Calculating Perimeters of Plane Shapes: Circles and Polygons and more Study Guides, Projects, Research Mathematics in PDF only on Docsity!
CONNECT: Areas, Perimeters
2. PERIMETERS OF PLANE SHAPES
A plane figure or shape is a two-dimensional, flat shape. This means that any plane shape has an outside and an inside. The perimeter of a plane shape literally means the measurement (meter) around (peri) the boundary of that shape. In other words, you could walk all around the shape, exactly on the boundary, counting your paces as you walk. When you reach your starting point, the number of paces would be the perimeter of the shape!
Of course, if you then compared YOUR measurement (using your paces) to someone elseโs measurement (in their paces), the two results are hardly likely to be the same and so we generally measure perimeter in any standard unit of length such as metres (m), centimetres (cm), millimetres (mm), or kilometres (km). (If you know how long your pace is, you could convert your number of paces to a standard measure.)
Special case: the perimeter of a circle is its circumference.
Diagram retrieved 22 January 2013 from http://en.wikipedia.org/wiki/Circle
There is a formula to calculate the length of the circumference (that is, the
perimeter of a circle). It is ๐ถ = 2๐๐ units, where ๐ถ units is the length of the
circumference and ๐ units is the length of the radius. ๐ is the number that
results when you divide the length of the circumference of a circle by the length of the diameter of that circle and is 3.141592654โฆ.
If you use the diameter instead of the radius to calculate the circumference
the formula is given by ๐ถ = ๐๐ units, where the length of the diameter is ๐
units and the length of the circumference is ๐ถunits.
When calculating the perimeter of a polygon , that is a plane figure that has straight sides, we can add the lengths of all the sides together, making sure that they are all stated using a consistent unit of measurement (no mixing of cm, mm, m etc).
Examples. Calculate the perimeters of these figures.
= 36mm
Over the page are some for you to try. If the figure consists of more than one shape, just remember that the perimeter is found by walking around the outside โ pretend you can do that on the paper. You can check your results with the solutions at the end of this handout.
12mm 12mm
12mm
12mm
6mm
Perimeter (circumference) = 2 ๐๐ cm
= 2 x ๐ x 5 cm
= 31.416 cm (rounded)
Perimeter = 12mm + 12mm + 12 mm
Perimeter = 12mm + 6mm + 12mm + 6mm = 36mm
One last problem to think about: True or false? All rectangles that have the same area must have the same perimeter. (Hint: Draw some rectangles that all have an area of 24cm^2 , for example, and work out their perimeter.)
If you need help with any of the Maths covered in this resource (or any other Maths topics), you can make an appointment with Learning Development through Reception: phone (02) 4221 3977, or Level 3 (top floor), Building 11, or through your campus.
Solutions
8cm
Perimeter = 8cm + 8cm + 8cm + 8cm =32cm
Perimeter = 21mm + 13mm + 21mm + 13mm = 68mm
8cm
21mm
13mm
Now we can add all the lengths together. For the top and the bottom, we get 9cm each. The right side is 6cm, the left is 5cm. It is only the pieces in between we need to worry about!
I found the perimeter is 34cm (9cm + 9cm + 6cm + 5cm + 2cm + 3cm).
Perimeter (circumference) = 2 ๐๐ m
= 2 x ฯ x 20 m
= 125.664m (rounded)
The 2cm is because the total length of the top of the shape has to be the same as the bottom length because it was originally a rectangle. We actually do not need to calculate it though because we know the total length across the top is 9cm!
2cm
