Free Mensuration 03 Practice Test - 6th grade 

In order to fence a land, a farmer needs the total length of the boundary which is given by the perimeter.

For ploughing and watering the land, a farmer needs the area of the field, and for excavating the land the farmer will need the volume of the soil excavated.

The amount of surface enclosed by a closed figure is called its area. An area expresses the extent of a two-dimensional figure.

Among the given options, $m^2$, $c{m}^2$ and $k{m}^2$ are all units of area while $m^3$ is a unit of volume.

Hence, $m^3$ is not a unit of area.

Area of a rectangle = Length $\times$ Breadth
                                $=10\times 7$
                                $=70c{m}^2$
When we join several figures, the area of the figure formed is the sum of areas of the figures joined.
Hence, area of the larger rectangle
$=12\times 70$
$=840c{m}^2$

Given, perimeter of a square land = 20 m
Perimeter of a square = 4 $\times$ Side of the square
$\therefore$ 20 = 4 $\times$ side
$\Rightarrow$ Side = $\frac{20}{4}$
             = 5 m
$\because$ Cow is standing at centre of the square, in order to go out it has to travel the length equal to half of the side =$\frac{5}{2}$
        = 2.5 m

Area of square = side $\times$ side
$\therefore$ side $\times$ side = 4 cm²
$\Rightarrow$ side = 2 cm

Now,
Length of the bigger rectangle = 5 $\times$ 2
                                                    = 10 cm
Breadth of the bigger rectangle = 2 $\times$ 2
                                                      = 4 cm
$\therefore$ Perimeter of the bigger rectangle
= 2( Length + Breadth)
= 2(10 + 4)
= 28 cm

The area of the figure is the sum of areas of all rectangles forming the figure.

Looking at the figure there are 4 rectangles, 3 rectangles of dimensions 3 m and 4m and 1 rectangle of dimensions 3 m and 7 m.
$\therefore$ Area = (3 $\times$ 4)+ (3 $\times$ 4) + (3 $\times$ 4) + (3 $\times$ 7) + (3 $\times$ 3)
                          = 12 + 12 + 12 +21 + 9
                          = 66 sq. units

Given, Area of circle = 36 cm²
Area of rectangle = $\frac{\text{Area of circle}}{6}$....(given)
                              = $\frac{36}{6}$ 
                              = 6 cm²
$\because$ Area of rectangle = length x breadth 
$\Rightarrow$ 6 = length x 1

So, length = 6 cm

On dividing the figure into squares and rectangle, it will look like:

The are of figure is sum of areas of square 1 and  rectangles 2 and 3.

=(1 x 1) + ( 4 x 5 ) + (3 x 5 ) 
= 1 + 20 + 15 
= 36 sq. units