Question

Find the perimeter of the given figure.

Answer 1

Hint: We will use the formula of the perimeter of circle \[2\pi x\] to solve this question. As the radius of the circle is given x. Then we will find the perimeter of the figure by subtracting the perimeter of the missing part. In case of circle, perimeter and circumference is the same.

Complete step-by-step answer:
Before proceeding with the question we should understand the concept of perimeter.
In geometry, perimeter can be defined as the path or the boundary that surrounds a shape. It can also be defined as the length of the outline of a shape. Perimeter is the total length of the sides of a two dimensional shape. We often find the perimeter when putting up Christmas lights around the house or fencing the backyard garden.
Now from the given figure we can see that the radius of the circle is x cm. And we also know that the perimeter of the circle is \[2\pi x\].
And we can see from the figure that one-fourth of the circle is missing. Hence the perimeter of the figure will be the perimeter of the full circle minus the perimeter of one-fourth part. Using this information we get,
Perimeter of the figure \[=2\pi x-\dfrac{1}{4}(2\pi x)=\pi x\left( 2-\dfrac{1}{2} \right)=\dfrac{3}{2}\pi x......(1)\]
Hence the perimeter of the given figure is \[\dfrac{3}{2}\pi x\].

Note: Remembering the formula of the circumference(perimeter) is the key here. Also we should know that the perimeter of the circle is also its circumference. We in a hurry can make a mistake in solving equation (1) by subtracting half of the circumference of the circle instead of one-fourth and so we need to be careful while doing this step. Try not to do any calculation errors.