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4.5 B) Perimeter
4.5 B) Perimeter
The perimeter of a 2D shape is the total distance around the outside of the shape. The best way to think of a perimeter is that you start at one corner of the shape and walk around the outside of the shape until you reach the corner of the shape where you originally started from. The distance that you walk is the perimeter of the shape. Let’s have a few examples.
Example 1
What is the perimeter of the following rectangle?
What is the perimeter of the following rectangle?
The shape is a rectangle, which means that the top and the bottom are going to be the same length. Also, the left side of the shape is going to be the same length as the right side of the shape.
Let’s start from the bottom left corner and start walking towards the right. It is 9 m to get to the bottom right corner. We now walk upwards, and it is 4 m to get to the top right corner. We now walk to the top left corner, which is 9 m. And finally, we walk back to where we started (the bottom left corner), which is 4 m. Therefore, we have walked a total of:
Essentially, we just add all of the sides of the shape together.
Example 2
We have a regular octagon that has sides with a length of 6 cm. What is the perimeter of this shape?
We have a regular octagon that has sides with a length of 6 cm. What is the perimeter of this shape?
The shape is a regular octagon, which means that the length of all of the sides in the octagon are the same; all of the sides are 6 cm. An octagon has 8 sides and all of these sides have a length of 6 cm. Therefore, we can work out the perimeter of this regular octagon by multiplying 8 by 6 cm.
The perimeter of the regular octagon is 48 cm.
Example 3
Sometimes it will be the case that you are giving the perimeter of a shape and asked to work out a missing length or missing lengths.
For example, a regular hexagon has a perimeter of 72 mm. What is the length of each side in the regular hexagon?
We know that a hexagon has 6 sides. Also, this is a regular shape, which means that all 6 of the sides will be the same length. Therefore, 6 x the length of a side is equal to the perimeter (72 mm). This gives us the following equation:
Sometimes it will be the case that you are giving the perimeter of a shape and asked to work out a missing length or missing lengths.
For example, a regular hexagon has a perimeter of 72 mm. What is the length of each side in the regular hexagon?
We know that a hexagon has 6 sides. Also, this is a regular shape, which means that all 6 of the sides will be the same length. Therefore, 6 x the length of a side is equal to the perimeter (72 mm). This gives us the following equation:
We want to obtain the length of one of the sides, so we divide both sides of this equation by 6.
This means that the length of each of the sides in this regular hexagon is 12 mm.