# Free Mensuration 03 Practice Test - 6th grade

The idea of perimeter plays an important for ____.

A.

a farmer who wants to fence his land

B.

a farmer who wants to plough his land

C.

a farmer who wants to excavate his land

D.

a farmer who wants to water his land

#### SOLUTION

Solution : A

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 _____.

A.

perimeter

B.

area

C.

volume

D.

height

#### SOLUTION

Solution : B

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

Which of the following is not the unit of area?

A.

m2

B.

cm2

C.

km2

D.

m3

#### SOLUTION

Solution : D

Among the given options, m2, cm2 and km2 are all units of area while m3 is a unit of volume.

Hence, m3 is not a unit of area.

The length of a rectangle is 10 cm and width is 7 cm. What will be the area of a rectangle formed by joining 12 such rectangles?

A.

840 cm2

B.

70 cm

C.

680 cm2

D.

460 cm

#### SOLUTION

Solution : A

Area of a rectangle = Length × Breadth
=10×7
=70 cm2
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
=12×70
=840 cm2

A piece of square land has a perimeter equal to 20 m. A cow is standing in the middle of the square land as shown in the figure. What is the minimum distance the cow has to travel in order to go out of the field and drink water? A.

5 m

B.

2.5 m

C.

4 m

D.

20 m

#### SOLUTION

Solution : B

Given, perimeter of a square land = 20 m
Perimeter of a square = 4 × Side of the square
20 = 4 × side
Side = 204
= 5 m
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 =52
= 2.5 m

The area of each square is in the given figure is 4 cm2. The perimeter of the whole figure will be A.

24 cm

B.

28 cm

C.

20 cm

D.

44 cm

#### SOLUTION

Solution : B

Area of square = side × side
side × side = 4 cm2
side = 2 cm

Now,
Length of the bigger rectangle = 5 × 2
= 10 cm
Breadth of the bigger rectangle = 2 × 2
= 4 cm
Perimeter of the bigger rectangle
= 2( Length + Breadth)
= 2(10 + 4)
= 28 cm

The area of the given figure will be A.

94 sq.units

B.

66 sq.units

C.

90 sq.units

D.

93 sq.units

#### SOLUTION

Solution : B 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.
Area = (3 × 4)+ (3 × 4) + (3 × 4) + (3 × 7) + (3 × 3)
= 12 + 12 + 12 +21 + 9
= 66 sq. units

Given the area of a circle is 36 cm2. The area of the rectangle is 16th of the area of the circle. If the breadth of the rectangle is 1 cm, what is the length?

A.

6 cm

B.

12 cm

C.

36 cm

D.

26 cm

#### SOLUTION

Solution : A

Given, Area of circle = 36 cm2
Area of rectangle = Area of circle6....(given)
= 366
= 6 cm2
Area of rectangle = length x breadth
6 = length x 1

So, length = 6 cm

The area of a square is 16 cm2 What will be the area of the rectangle with length equal to double the side of the square and width equal to half of the side of the square?

A. 16 cm2
B. 20 cm2
C. 24 cm2
D. 36 cm2

#### SOLUTION

Solution : A

Area of square = side × side = 16 cm2
side of square = 4 cm
Length of rectangle = 8 cm and breadth = 2 cm
Area of rectangle = 8 × 2 = 16 cm2

The area of the given figure (all dimensions in units) will be A.

46 sq. units

B.

60 sq. units

C.

36 sq. units

D.

63 sq. units

#### SOLUTION

Solution : C

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