How can we find the perimeter of this figure?
According to the steps for finding the perimeter of a composite figure, we should find the length of any unknown side and then add up the lengths of all the sides to get the perimeter.
Hence, for this figure, the perimeter is given by
42 plus 21 plus 42 plus 21 and so on.
There are many numbers involved in this addition.
Hence, the calculation is tedious and it’s easy to make mistake in the calculation.
Is there a better method to find the perimeter of this figure?
Well, an easier method is to shift some of the sides of the figure.
Do you have any idea how we can shift the sides of the figure?
First, we can shift all the horizontal sides of the figure up.
This forms a continuous horizontal line at the top.
Likewise, we can shift all the vertical sides to the right so that they form a continuous vertical line.
Now, what do you see?
Do you see that the perimeter of the figure is in fact the same as the perimeter of a rectangle?
So, first we find the length and the breadth of the rectangle.
The length of the rectangle is given by 42 multiplied by 6.
This works out to 252 centimetres.
Its breadth is equal to 21 multiplied by 6
which works out to 126 centimetres.
The perimeter of the figure which is the same as the perimeter of the rectangle is equal to
2 times the sum of 126 and 252.
This gives us 756 centimetres.
Therefore, the perimeter of the figure is
756 centimetres.