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