Question

Find the perimeter of the following figure. ($\pi = 3.14$)

  

Answer 1

Hint- Here we will be using the formulas which are perimeter of the rectangle\[ = 2\left( {{\text{Length}} + {\text{Breadth}}} \right)\] and perimeter of the semicircle$ = \pi r$ in order to find the perimeter of the given figure.

Complete step-by-step solution -
From the above figure, we can conclude
Length of the rectangle ABCD, AB=16 cm
Breadth of the rectangle ABCD, BC=3 cm
Also, there are two semicircles whose diameters are the sides AB and CD of the rectangle ABCD
So, diameter of both the semicircles is equal to 16 cm i.e., d=16 cm
As we know that radius=$\dfrac{{{\text{diameter}}}}{2}$
Radius of both the semicircles is r=$\dfrac{{\text{d}}}{2} = \dfrac{{16}}{2} = 8$ cm
Also, perimeter of any rectangle\[ = 2\left( {{\text{Length}} + {\text{Breadth}}} \right)\]
Perimeter of rectangle ABCD is given by
\[{{\text{P}}_1} = 2\left( {{\text{AB}} + {\text{BC}}} \right) = 2\left( {16 + 3} \right) = 2 \times 19 = 38\] cm
Also, Perimeter of a semicircle with radius r is equal to $\pi r$
Perimeter of both the semicircles given with radius r=8 cm is given by
${{\text{P}}_2} = 2 \times \left( {\pi r} \right) = 2 \times 3.14 \times 8 = 50.24$ cm
Perimeter of the figure is equal to the sum of the perimeter of the rectangle ABCD and the perimeter of the two given semicircles.
i.e., Required perimeter$ = {{\text{P}}_1} + {{\text{P}}_2} = 38 + 50.24 = 88.24$ cm.

Note- In this particular problem, the two given semicircles are of the same diameter (or of the same radius) so instead of calculating the perimeters of the two semicircles separately we can find the perimeter of one semicircle and then multiply that with two which is done in the above solution.