Mensuration Worksheet

        Subjective Questions

1. Rani bought a table cloth for her table (refer the top view of the table), but the cloth kept falling off from the table. As a result she decided to put a lace all around the table cover. Now if the lace required was 4m, then find the length of the table.
   
   
   
2. Rohan likes to run every morning, as it keeps him fit and healthy. He takes 10 rounds of a rectangular running track (refer the image below). Find the total distance covered by him.
   
   
   
3. Ram has a garden (refer the top view of the garden), where he grows beautiful flowers. Now from the past few days, there has been an increased nuisance of stray dogs, who would enter his garden and damage his flowers. So he has decided to fence his garden and the rate of fencing is Rs.20 per metre. Now find the total cost of fencing the garden.
   
   
   
4. Rahul is a cat lover and wanted to stick the poster of two cute cats on his wall (refer picture below). Now to stick this to the wall, a tape is used all around the poster. Find the minimum length of tape required by Rahul.
   
   
   
5. Ameya’s family bought a new house. They conducted a pooja for the new house. Now the priest who conducted the pooja drew a Swastika on the floor (refer the image). Ameya was fascinated by its design and draws one in his note book. Next day his teacher saw the Swastika symbol and asks Ameya to find the length of the boundaries of his Swastika. What will be Ameya’s answer?
   
   
   
6. Kiran was playing in the park when he noticed a beautiful leaf. This leaf was perfectly symmetrical. Now Kiran brings this leaf to his house and decides to measure its area using a graph paper made up of squares of area 1 cm2. He places the leaf on the graph paper as shown, now help Kiran to find the answer.
   
   
   
7. Rashi visited a hospital for a routine check-up, there she saw a plus symbol on the ambulance as shown below. Now Rashi has just learnt the process of finding the area of a shape by dividing it into squares and rectangles. Now using this method, help Rashi to find the area of the plus symbol.
   
   
   
8. Ravi is interested in architecture and he draws the plan of floors in his free time. One day he drew the rough plan of his school’s ground floor (refer the image for details). Now Ravi was exited and he showed his drawing to his class teacher. The class teacher was very much impressed, but his teacher wanted to know the area of the floor. Help Ravi to find the area.
   
    
9. Arjun is a ^fan of boxing. One day he went to see a live boxing match. Before the start of the match, Arjun was observing the boxing ring (it is called a ring, but actually it is a square), he found that there are 4 ropes that are tied around the four corners. Arjun was wondering about the total length of ropes used to create this ring. Now if the length of one rope at one side of the ring is 700 cm, then help Arjun find the total length of the rope used.
   
   
   
10. Atul visits a country fair, there he finds a giant Ferris wheel in the form of a regular hexagon (refer image below). Now the length of the diagonal of the wheel is given to be 500 meters. If so help Atul to find the perimeter of the Ferris wheel.
    
    
    Multiple Choice Questions
    
    
11. If the length and breadth of a rectangle is represented by l and b respectively, then which of the following will represent its perimeter?
    (a)2(l×b)
    (b)2l+b
    (c)2l+2b
    (d)2b + l
    
    
12. Rahim bought a square craft paper of side 10 cm. Now he folds the paper in half vertically and then again folds the paper in half horizontally. Now the perimeter of the folded paper will be equal to
    
    (a)40 cm
    (b)30 cm
    (c)25 cm
    (d)20 cm
    
    
13. A mason had constructed stairs, whose side view was drawn by Noor (refer image below). Now, the mason had used square bricks of 30 cm side to construct the steps. Help Noor to find the perimeter of the side view of stairs.
    
    (a)360 cm
    (b)330 cm
    (c)300 cm
    (d)270 cm
    
    
14. A rectangular sheet of a paper having length 50 cm and breadth 25cm is cut in half along its length. Now the area of one half will be equal to
    
    (a)15 cm²
    (b)25 cm²
    (c)50 cm²
    (d)70 cm²
    
    
15. A Square container of side 60 cm is filled with water, the water is filled at the rate of 10 cm per min. After 5 min the water is stopped and the container is viewed from the side as shown. Calculate the area of the blue shape as seen from the side view.
    
    (a)360 cm²
    (b)340 cm²
    (c)320 cm²
    (d)300 cm²
    
    
16. Calculate the area of the following figure if the sides of the squares in the gird is 2cm.
    
    (a)60 cm²
    (b)40 cm²
    (c)20 cm²
    (d)30 cm²
    
    
17. Pavan runs around a square race track and covers a distance of 240 m in 3 rounds. So, the side of this square track will measure ____.
    
    (a)80 cm
    (b)40 cm
    (c)20 cm
    (d)10 cm
    
    
18. Raju was packing gift for his father on the occasion of his father’s birthday. He puts the gift in a rectangular box (refer image below), covered it and sealed it all round with an adhesive tape, twice. Find the minimum length of the adhesive tape required.
    
    (a)280 cm
    (b)120 cm
    (c)240 cm
    (d)140 cm
    
    
19. If the perimeter of below figure is 20 cm, then find the value of “x”
    
    (a)1 cm
    (b)2 cm
    (c)3 cm
    (d)4 cm
    
    
20. A folded square paper having side 4 cm (when folded), is unfolded to form the square as shown below. Find the measure of the unknown side of the unfolded paper
    
    (a)4 cm
    (b)8 cm
    (c)16 cm
    (d)24 cm

        Subjective Questions

1. Rani bought a table cloth for her table (refer the top view of the table), but the cloth kept falling off from the table. As a result she decided to put a lace all around the table cover. Now if the lace required was 4m, then find the length of the table.
   
   Solution:
   The table is in the form of a square.
   Hence, the lace will cover the border of the table, meaning the perimeter of the table.
   Perimeter of square = 4×side
   Length of lace = 4×side
   4 = 4 × side
    side = 1 m.
   
   
2. Rohan likes to run every morning, as it keeps him fit and healthy. He takes 10 rounds of a rectangular running track (refer the image below). Find the total distance covered by him.
   
   Solution:
   Length of track = 60 m
   Width of track = 30 m
   Total distance covered by Rohan in one round = perimeter of park (rectangle)
   = 2 (length + breadth)
   = 2 (60 + 30)
   = 2 (90)
   = 180m
    Total distance covered by Rohan in 10 rounds = 180×10 = 1800 m = 1.8 km
   
   
3. Ram has a garden (refer the top view of the garden), where he grows beautiful flowers. Now from the past few days, there has been an increased nuisance of stray dogs, who would enter his garden and damage his flowers. So he has decided to fence his garden and the rate of fencing is Rs.20 per metre. Now find the total cost of fencing the garden.
   
   Solution:
   Length of garden = 50 m
   Width of garden = 30 m
   To find the cost of fencing we need to find the perimeter of garden
    Perimeter of garden (rectangle)
   = 2 (length + breadth)
   = 2 (50 + 20)
   = 2 (70)
   = 140m
   Now cost of fencing 1 m park = Rs. 20
   Total cost of fencing the park = 140×20 = Rs. 2800
   
   
4. Rahul is a cat lover and wanted to stick the poster of two cute cats on his wall (refer picture below). Now to stick this to the wall, a tape is used all around the poster. Find the minimum length of tape required by Rahul.
   
   Solution:
   The poster is in the form of a square.
   Hence, the minimum length of tape required will be equal to the perimeter of the square
   = 4 × length of one side
   = 4 × 30
   = 120 cm
   
   
5. Ameya’s family bought a new house. They conducted a pooja for the new house. Now the priest who conducted the pooja drew a Swastika on the floor (refer the image). Ameya was fascinated by its design and draws one in his note book. Next day his teacher saw the Swastika symbol and asks Ameya to find the length of the boundaries of his Swastika. What will be Ameya’s answer?
   
   Solution:
   The sum of lengths of Swastika = length of its boundary
   = 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3
   =52 cm
   Hence, Ameya’s answer will be 52 cm
   
   
6. Kiran was playing in the park when he noticed a beautiful leaf. This leaf was perfectly symmetrical. Now Kiran brings this leaf to his house and decides to measure its area using a graph paper made up of squares of area 1 cm2. He places the leaf on the graph paper as shown, now help Kiran to find the answer.
   
   Solution:
   
   Kiran can find the area as follows
   
   Hence, the area of the leaf is approximately 13 sq. cm.
   
   
7. Rashi visited a hospital for a routine check-up, there she saw a plus symbol on the ambulance as shown below. Now Rashi has just learnt the process of finding the area of a shape by dividing it into squares and rectangles. Now using this method, help Rashi to find the area of the plus symbol.
   
   Solution:
   The plus symbol is made up of 5 squares each with side 5cm.
   
   Hence the area of the plus symbol = 5 × area of one square
   Area of one square = side × side
   = 5 × 5
   = 25 sq. cm.|
   Thus, area of plus symbol = 5 × 25 = 125 sq.cm.
   
   
8. Ravi is interested in architecture and he draws the plan of floors in his free time. One day he drew the rough plan of his school’s ground floor (refer the image for details). Now Ravi was exited and he showed his drawing to his class teacher. The class teacher was very much impressed, but his teacher wanted to know the area of the floor. Help Ravi to find the area.
   
   Solution:
   The floor plan can be broken into individual areas as shown
   
   Hence the area of the floor = Area of 3 rectangles = 5×4 + 4×10 + 6×4
   = 20 + 40 + 24
   = 84 sq. cm
   Hence, the area of the floor plan is 84 sq. cm
   
   
9. Arjun is a ^fan of boxing. One day he went to see a live boxing match. Before the start of the match, Arjun was observing the boxing ring (it is called a ring, but actually it is a square), he found that there are 4 ropes that are tied around the four corners. Arjun was wondering about the total length of ropes used to create this ring. Now if the length of one rope at one side of the ring is 700 cm, then help Arjun find the total length of the rope used.
   
   Solution:
   A boxing ring is shaped like a square with all four sides equal.
   
   Now the length of one side of this square is given to be 700 cm
   Hence one turn of rope = perimeter of the square with side 700 cm
   = 4×side
   =4×700
   =2800
   Now, there are 4 such squares
   Hence, total length of rope used = 4× One turn of rope
   =4×2800
   =11,200 cm
   Thus the total length of rope used is 11,200 cm
   
   
10. Atul visits a country fair, there he finds a giant Ferris wheel in the form of a regular hexagon (refer image below). Now the length of the diagonal of the wheel is given to be 500 meters. If so help Atul to find the perimeter of the Ferris wheel.
    
    Solution:
    For a regular hexagon, length of its diagonal is twice the length of one of its sides
    
    Hence,
    Length of diagonal = 2× one side
    500 =2× one side
     One side = 250 m
    Also, all sides of a regular hexagon is equal
    Hence the perimeter of regular hexagon = 5× one side
    = 5 × 250
    = 1250 m
    
    Multiple Choice Questions
    
    
11. If the length and breadth of a rectangle is represented by l and b respectively, then which of the following will represent its perimeter?
    (a)2(l×b)
    (b)2l+b
    (c)2l+2b
    (d)2b + l
    Correct option: (c) 2l + 2b
    Solution:
    We can visualize the given rectangle as shown
    
    Hence, sum of its sides = l + b + l + b
    = 2l + 2b
    
    
12. Rahim bought a square craft paper of side 10 cm. Now he folds the paper in half vertically and then again folds the paper in half horizontally. Now the perimeter of the folded paper will be equal to
    
    (a)40 cm
    (b)30 cm
    (c)25 cm
    (d)20 cm
    Correct option: (d) 20 cm
    Solution:
    Perimeter of a Square = 4 × one side
    
    Refer to the above diagram, it is mentioned with the sides
    We can see that after folding twice, the sides of the square will be reduced to 5, that is they are halved.
    Hence, the perimeter = 4×5 = 20 cm.
    
    
13. A mason had constructed stairs, whose side view was drawn by Noor (refer image below). Now, the mason had used square bricks of 30 cm side to construct the steps. Help Noor to find the perimeter of the side view of stairs.
    
    (a)360 cm
    (b)330 cm
    (c)300 cm
    (d)270 cm
    Correct option: (a) 360 cm
    Solution:
    Perimeter is the outer boundary of the figure. Here outer boundary is denoted as shown.
     
    Hence the perimeter of the given figure will be 12×30, as shown belo
     
    ∴ Perimeter = 360 cm
    
    
14. A rectangular sheet of a paper having length 50 cm and breadth 25cm is cut in half along its length. Now the area of one half will be equal to
    
    (a)15 cm²
    (b)25 cm²
    (c)50 cm²
    (d)70 cm²
    Correct option: (b) 25 cm²
    Solution:
    Here on dividing the rectangle along its length, we get a figure with length and breadth both equal to 5cm
    
    Hence, we get a square
    So, area of a square = side × side
    = 5 × 5
    = 25 cm²
    
15. A Square container of side 60 cm is filled with water, the water is filled at the rate of 10 cm per min. After 5 min the water is stopped and the container is viewed from the side as shown. Calculate the area of the blue shape as seen from the side view.
    
    (a)360 cm²
    (b)340 cm²
    (c)320 cm²
    (d)300 cm²
    Correct option: (d) 300 cm²
    Solution:
    The water is filled at the rate of 10 cm per min.
    Which means,
    1 min = 10 cm water filled
    ∴ 5 min = 5 × 10 = 50 cm water filled
    Hence the breadth will be 50 cm
    
    Hence we have a rectangle, whose area is given by length × breadth
    ∴ Area of blue shape = 60 × 50 = 300 cm
    
    
16. Calculate the area of the following figure if the sides of the squares in the gird is 2cm.
    
    (a)60 cm²
    (b)40 cm²
    (c)20 cm²
    (d)30 cm²
    Correct option: (c) 20 cm²
    Solution:
    
    From the figure we can calculate the number of full and half squares, and then we can multiply them with area of a single square which is 2×2 = 4 sq.cm
    
    Hence the area of the figure = 20 sq.cm.
    
    
17. avan runs around a square race track and covers a distance of 240 m in 3 rounds. So, the side of this square track will measure ____.
    
    (a)80 cm
    (b)40 cm
    (c)20 cm
    (d)10 cm
    Correct option: (c) 20 cm
    Solution:
    Pavan runs 240m in 3 rounds|
    Hence,
    Distance covered = 3 × perimeter of Square race track
    ∴ 240 = 3 × 4 × side
    ∴ 240÷12 = side
    ∴ side = 20 m
    Hence, the side of the square race track will be 20m.
    
    
18. Raju was packing gift for his father on the occasion of his father’s birthday. He puts the gift in a rectangular box (refer image below), covered it and sealed it all round with an adhesive tape, twice. Find the minimum length of the adhesive tape required.
    
    (a)280 cm
    (b)120 cm
    (c)240 cm
    (d)140 cm
    Correct option: (c) 240 cm
    Solution:
    The length of tape required to wrap around the rectangular box once = perimeter of the rectangle
    = 2 (length + breadth)
    = 2(40 + 20)
    = 120 cm
    Now, to wrap the tape twice, we need twice the length of tape which is required to wrap it once.
    Hence, the length of tape required to wrap around the rectangular box twice
    = 120 × 2 = 240 cm
    
    
19. If the perimeter of below figure is 20 cm, then find the value of “x”
    
    (a)1 cm
    (b)2 cm
    (c)3 cm
    (d)4 cm
    Correct option: (b) 2 cm
    Solution:
    Perimeter of a closed figure = sum of the length of its outer boundary
    ∴ 20 = X + 5 + 1 + 3 + 3 + 1 + 5
    ∴ 20 = X + 18
    ∴ 20 – 18 = X
    ∴ X = 2 cm
    
    
20. A folded square paper having side 4 cm (when folded), is unfolded to form the square as shown below. Find the measure of the unknown side of the unfolded paper
    
    (a)4 cm
    (b)8 cm
    (c)16 cm
    (d)24 cm
    Correct option: (b) 8 cm
    Solution:
    The figure formed after unfolding will be square, having side twice that of the folded square.
    
    Hence the measure of the unknown side of the unfolded paper is 8cm.