Question

Find the area of unshaded portion of the figure, the shaded portion being semicircular regions:

A. $ 100.5{m^2} $
B. $ 101.5{m^2} $
C. $ 201.5{m^2} $
D. $ 101.8{m^2} $

Answer 1

Hint: In order to solve this question we will first find the area of the shaded region then we will find the area whole area and further we will subtract the area of the shaded region to the whole area and we will get the area of the unshaded part of the region for this we will have to find the radius of the semicircle first.

Complete step by step solution:
For solving this question we will first find the area of the whole region so for this let us analyze that this is a rectangle so for finding the area of the rectangle we will have to multiply the length and breath:
Area of the whole region:
Area of rectangle = $ 14 \times 10 $
On further solving this we will get:
Area of rectangle = $ 140{m^2} $
Now we will have to find the area of the shaded region for this we will have to find the radius of the semicircular region, since the whole length is equal to 14 m and the number of semicircles are two so there are two diameter it means twice of diameter = 14m so we in place of diameter we will put $ r = \dfrac{d}{2} $
So $ d = 7 $
Putting the value of d in this equation from the above equation we will get:
 $ r = \dfrac{7}{2} $
Now as we know the area of semicircle is $ \dfrac{{\pi {r^2}}}{2} $ so putting all the values we will get:
Area of semicircle = $ \dfrac{1}{2} \times \dfrac{{22}}{7} \times \dfrac{7}{2} \times \dfrac{7}{2} $
On further solving this we will get the value of:
Area of semicircle = $ \dfrac{{77}}{4} $
Since there are 2 such semicircles so the area of shaded part will be = $ \dfrac{{77}}{2} $
So on finalizing it we will get area of the shaded part = $ 38.5{m^2} $
Now the area of the unshaded portion will be $ 140 - 38.5 $
On further solving it will get the area of the unshaded portion will be = $ 101.5{m^2} $
So the correct option will be B.
So, the correct answer is “Option B”.

Note: While solving these types of questions we should always keep in mind while we find the area of the semicircle we will have to keep in mind that there are two semicircles and the area which we have to find is unshaded so these things should be kept in mind because while solving the question in hurry we do not multiply by 2 as there are two semicircles.