Question

Question: A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig 20.23. If AB=60 m and BC=28 m, find the area of the plot.

Answer 1

Hint: A rectangle is a shape that consists of four sides and opposite sides is equal in length or width. Each side is denoted with an alphabet in the above diagram. A semicircle is an exact half of a circle; it means a semi-circle occupies half the area that a circle has. Here, the plot is the combination of a rectangle and a semi-circle so add the areas of the both rectangle and the semi-circle to find the whole area of the plot.

Complete step-by-step answer:
The length of the rectangle is \[l = 60\;{\rm{m}}\].
The width of the rectangle is \[w = 28\;{\rm{m}}\].
As per the diagram, we can observe that the width of the rectangle is equal to the diameter of the semi-circle or half of the width is equal to the radius of the semi-circle.
We will find the radius of the semicircle by using the expression.
\[\begin{array}{l}
r = \dfrac{{BC}}{2}\\
r = \dfrac{{28}}{2}\\
r = 14\;{\rm{m}}
\end{array}\]
The sum of the area of the rectangle and the area of the semi-circle gives the area of the plot, then we know the equation to find the area of the plot is given as,
\[A = \left( {l \times w} \right) + \left( {\dfrac{\pi }{2}{r^2}} \right)\]
On substituting the values in the above equation, we get the value of area as,
\[\begin{array}{c}
{A_1} = \left( {60\;{\rm{m}} \times 28\;{\rm{m}}} \right) + \left( {\dfrac{\pi }{2}{{\left( {14\;{\rm{m}}} \right)}^2}} \right)\\
 = 1680 + 307.72\\
 = 1987.72\;{{\rm{m}}^2}
\end{array}\]
Therefore, the area of the whole plot is \[1987.72\;{{\rm{m}}^2}\].

Note: In the solution, it is given a combination of the rectangle and a semi-circle, so we need to take both areas and while taking the area of the semicircle be sure it is the half of the circle. While substituting the values in the equation, it is noted that all the units are in the same level, for suppose, if the unit of length is in meters and the width of the rectangle is in centimeters then convert the width into meters or convert the meters of length into centimeters.