Question

Find the perimeter of the section in the bold in the above figure.

Answer 1

Hint: The section of the figure which is marked in bold makes it a Semi-circle plus the length of the diameter. Perimeter is the length of the outline of the shape, and in case of the circle it is known as circumference represented as\[\pi d\], where $d$ is the diameter of the circle. Since the portion marked in bold is a semi-circle, then the circumference of semicircle becomes the half of the circumference of the circle given as \[P = \dfrac{{\pi d}}{2}\] and the bold section also contain a diameter of length \[d = 21\] will also be added.

Complete step by step answer:
Given the diameter of the circle is \[d = 21\]
In the given figure it can be clearly seen that the bold line is in only half section of the circle so we will have to find the circumference of half circle and length of diameter will be added.
\[
  {\text{P}} = \dfrac{{\pi d}}{2} + d \\
   = \dfrac{{22}}{7} \times \dfrac{{21}}{2} + 21 \\
   = \dfrac{{66}}{2} + 21 \\
   = 33 + 21 \\
   = 54 \\
 \]

So, the perimeter of the bold section is 54 cm.

The above-used formula could have also been written in terms of radius which is half of the diameter represented as\[r = \dfrac{d}{2}\], so the above formula in terms of radius could have been \[P = \pi r + 2r\]this is the other way to solve the question and the answer by this formula will be same.

Note: We can find the perimeter of a figure only when it is a close region. Here the diameter makes the figure a closed region, so the perimeter was found.