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Q.

The shape given below is in rectangular shape in the middle and semi-circular at the ends as shown in the diagram.


Question Image

Find the area and the perimeter of the above shape.


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a

Area =129.50 m 2  , Perimeter = 50m  

b

Area =50 m 2  , Perimeter =129.50 m  

c

Area =129.50 m 2  , Perimeter =48m  

d

Area =129.50 m 2  , Perimeter =50m  

answer is C.

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Detailed Solution

We have been given a shape that is in rectangular shape in the middle and semi-circular at the ends as shown in the diagram.
Question ImageLet us calculate the area of the semi-circle and the area of the rectangle.
It is clear from the above given figure that the diameter of semicircle =7m  .
So, the radius of semi-circle, (R) is half of its diameter.
  ⇒R= 7 2 =3.5m  
Length of rectangle (L) can be calculated as,
L=20−R−R ⇒L=20−(2R) ⇒L=20−(2×3.5) ⇒L=13m  
And, breadth of rectangle, B = diameter of semicircle =7m  
Area of rectangle = Length × Breadth
=13×7 =91 m 2  
Area of each semicircle is,
= π R 2 2 = π (3.5) 2 2 =19.25 m 2  
So,
Area of whole figure = Area of rectangle + Area of the two identical semicircles.
Therefore, total area of the figure =91+(2×19.25)=129.50 m 2  
Let us now calculate the perimeter of the figure given in the question.
Perimeter of the whole figure =   2 times the length of the rectangle + 2 times circumference of each semicircle.
Circumference of each semicircle is,
= 1 2 (2πR) = 1 2 (2π×3.5) =11m  
Therefore, perimeter of the above figure is,
=(2×13)+(2×11) =48m  
So, for the given figure, Area =129.50 m 2   and Perimeter =48m  .
Hence, option 3 is correct.
 
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