Question

Task 3 People of Khejadi village take good care of plants, trees and animals. They say that plants and animals can survive without us, but we cannot survive without them. Inspired by her elders, Amrita markets some land for her pets (camel and ox) and plants. Find the area kept for animals and plants in the living area and also the remaining area.

Answer 1

Hint: In figure we see that there are two types of shapes, rectangle and circle. To find areas in which animals and plants are kept we use formulas of mensuration related to corresponding figures to calculate area and finally to calculate remaining area we find the difference of total area and sum of the area covered to keep plants and animals.
Formulas used: Area of circle $ = \pi {r^2} $ , where ‘r’ is radius of the circle.
Area of rectangle $ = l \times b $ , where l is length and b is breadth of the rectangle.

Complete step by step solution:

From the figure we see that there is a big rectangle of length $ 15m\,\,and\,\,breadth\,\,10m $ , which is divided into different parts.
So, we first find the area of the big rectangle or total area.
Total area = Length $ \times $ Breadth
 $ = 15 \times 10 = 150{m^2} $
Area cover to keep plants is given as
Length $ \times $ Breadth
Therefore,
Area for plants $ = 9 \times 1 $
 $ = 9{m^2} $
Also, the area to keep the camel is also in the shape of a rectangle. Therefore, its area is given as: Length $ \times $ Breadth
Area for camel $ = 5 \times 3 = 15{m^2} $
Now, area to keep Ox is in circular shape and its area is given as: $ \pi {r^2},\,\,where\,\,r\,\,is\,\,\,radius\,\,of\,\,the\,\,cirle $
Area for $ Ox = \pi \times {\left( {1.4} \right)^2} = \dfrac{{22}}{7} \times 1.96 $
 $ = 6.16{m^2} $
Therefore, to find the remaining area we first find the sum of areas of plants, camel and ox. Which is given as:
 $
  9 + 15 + 6.16 \\
   = 30.16 \;
  $
Therefore, the remaining area of the figure is given as difference of total area and area covered by three.
$ \Rightarrow$ Remaining area $ = 150 - 30.16 $
 $ = 119.84\,{m^2} $
Hence, from above we see that the remaining area of the figure is $ 119.84{m^2} $ .
So, the correct answer is “ $ 119.84{m^2} $ ”.

Note: Students must be very careful while doing mensuration problems as while doing these types of problems on should apply correct formulas related to given shapes and also see units of each term as in mensuration units must be same using different units might leads to wrong answer.