# Free Mensuration Subjective Test 01 Practice Test - 6th grade

### Question 1

Find the area of a rectangle whose length is 4 cm and its breadth is 3 cm. [1 MARK]

#### SOLUTION

Solution :Solution: 1 Mark

=4×3

Area of the rectangle = length × breadth

=12cm2

### Question 2

Find the area of the following figure (in sq. inches). [2 MARKS]

#### SOLUTION

Solution :Steps: 1 Mark

Answer: 1 Mark

Area of the given shape = Area of square + Area of rectangle

= (side)2 + (length × breadth)=(3)2+(2×9)=9+18

=27 sq inches

### Question 3

What is the area of the table whose sides measure 1m 20 cm in length and 2m 50 cm in breadth? [2 MARKS]

#### SOLUTION

Solution :Steps: 1 Mark

Answer: 1 Mark

⇒ Length (l) = 1m 20cm

1 m= 100 cm

= (1+20100)m=1.2m

⇒ Breadth (b) = 2m 50cm

= (2+50100)m=2.5m

⇒ Area = l×b=1.2 m×2.5 m=3 m2

### Question 4

The blackboard of Akshit's classroom has length 6m and its width is 5m. If it has to be framed by a steel plate at the borders, then what will be the length of steel plate required? [3 MARKS]

#### SOLUTION

Solution :Steps: 1 Mark

Formula: 1 Mark

Answer: 1 Mark

The perimeter of the blackboard = Length of the steel plate required.

Perimeter of a rectangle =2×(L+B).

Length of steel plate

= 2×(6+5)=2×11=22m

### Question 5

Find the perimeter and area of the shape given below: [3 MARKS]

#### SOLUTION

Solution :Concept: 1 Mark

Application: 1 Mark

Solution: 1 Mark

⇒ Perimeter = Length of the boundary

= (45 + 22 + 25 + 8 + 20 + (8+22))

= (45 + 22 + 25 + 8 + 20 + (30))

= 150m

⇒ Area of the shape = Area of the larger rectangle + area of smaller rectangle

=(45×22)+(20×8)

=(990)+(160)

=1150 cm2

∴ Area =1150cm2

### Question 6

Pratik and his friends were playing around a track that is shaped like a regular hexagon. Each side measures 45 feet. If they make 2 complete trips around the track, how far will they have walked? [3 MARKS]

#### SOLUTION

Solution :Steps: 1 Mark

Formula: 1 Mark

Answer: 1 Mark

The perimeter of a regular hexagon

= 6×side lengthPerimeter of the hexagon

= 6×45 feet

=270feetAs they walk 2 rounds:

∴ Distance covered

= 2×270feet

=540feet

### Question 7

Find the area of the following shape (in sq. cm) [4 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Formula: 1 Mark

Answer: 1 Mark

Area of the above shapes can be calculated in two steps:

i) Area of shape marked 1

ii) Area of shape marked 2⇒ Area of shape marked 1 = Area of rectangle

= length × breadth= 4 × 9

= 36 cm2

⇒Area of shape marked 2 = Area of triangle

= 12× base × height= 12× 6 × 4

= 12 cm2

⇒Area of shape = Area of shape marked 1+ Area of shape marked 2

= (36 + 12) cm2

= 48 cm2

### Question 8

Prashant wants to cover his kitchen shelf with square tiles of side 0.5 m. The kitchen shelf's dimensions being 4m by 3m. Find the number of tiles required. If each tile costs Rs 70, how much will he have to spend for covering his kitchen shelf?** **[4 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Formula: 1 Mark

Answer: 1 Mark

Area of one square tile = (side)2 = (0.5m)2 = 0.25 m2.Area of the kitchen shelf = length × breadth

= 4 × 3 = 12m

Number of tiles

= Area of kitchen shelfArea of square tile

= 120.25 = 48

Cost of 1 tile = Rs 70

Cost of 48 tiles = Rs 48 × 70 = Rs 3360

### Question 9

A large pizza has a circumference of 88 inches. What will be the smallest area of the box holding the pizza? [4 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Formula: 1 Mark

Answer: 1 Mark

Circumference of a circle

= 2×π×r=d×π=88 inches

Where, d = diameter and π=227

⇒88=227×d

⇒d=88×722

⇒d=28inches

The diameter of the pizza will be equal to the length of the side of the box.

Side of box = 28 inches

Area of the box = (side)2 = (28 inches)2 = 784 inches2

### Question 10

Split the below figures into multiple rectangles and find out their area. All dimensions are given in centimetres. [4 MARKS]

#### SOLUTION

Solution :Each Option: 2 Marks

(a) The above figures can be split into multiple rectangles as follows:

Area of 1st rectangle

=21×7=147 cm2

Area of 2nd rectangle

=7×7=49 cm2

Area of 3rd rectangle

=7×7=49 cm2

Total area of the whole figure

=147+49+49=245 cm2

(b) The above figures can be split into multiple rectangles as follows:

Area of 1st rectangle

=5×1=5 cm2

Area of 2nd rectangle

=4×1=4 cm2

Total area of the whole figure

=5+4=9 cm2