The perimeter of the blue figure is given by the sum of the lengths of all the sides in orange.
Do you think we can rearrange some of the sides to form a shape with perimeter that can be easily calculated?
Earlier, we have mentioned that the two quadrants are identical to a quadrant in the circle.
Hence, the length of the curved side of the two quadrants must be equal to the length of the curved side of a quadrant in the circle.
This means we can flip the curved sides of both quadrants over to form a complete circle.
Now, the perimeter of the blue part is simply equal to the sum of the circumference of the circle and the lengths of the two horizontal lines.
First, let’s work out the circumference of the circle.
This is equal to 22 over 7 multiplied by 28
which works out to 88 centimetres.
Next, the length of each horizontal line is given by
14 times 2 which is equal to 28 centimetres.
The perimeter of the blue part is hence equal to
28 plus 88 plus 28.
This works out to 144 centimetres.
Therefore, the perimeter of the blue part is
144 centimetres.