Grandmother’s Quilt Class 5 Solutions Question Answer Maths Chapter 11

Students often refer to Maths Mela Class 5 Solutions Chapter 11 Grandmother’s Quilt Question Answer NCERT Solutions to verify their answers.

Class 5 Maths Chapter 11 Grandmother’s Quilt Question Answer Solutions

Grandmother’s Quilt Class 5 Maths Solutions

Class 5 Maths Chapter 11 Solutions

Let Us Do (Page 142)

Question 1.
Find the perimeter of the following shapes. All sides of the following shapes are equal.

Solution:
(a) Figure is pentagon with 5 sides. (All sides are equal)
Side = 4 cm
Perimeter of a pentagon = Sum of all sides
= (4 + 4 + 4 + 4 + 4) cm
= 4 × 5 cm
= 20 cm

(b) Side = 5 cm (All sides are equal)
Perimeter = Sum of all sides
= (5 + 5 + 5 + 5 + 5 + 5) cm
= 5 × 6 cm
= 30 cm

Question 2.
Draw two rectangles each having the following perimeters,
(a) 26 cm
Solution:

Perimeter = Sum of all sides
= (8 + 5 + 8 + 5) cm
= (2 × 8) + (2 × 5) cm
= 16 + 10
= 26 cm

(b) 18 cm
Solution:

Perimeter = Sum of all sides
= (5 + 4 + 5 + 4) cm
= (10 + 8) cm
= 18 cm

NCERT (Page 143)

How many patches have they used to make rug?

Solution:
No. of patches = 6 × 1 5 = 90 square patches
[Count all squares patches in a rug.]

They found that __________, __________ and __________ shapes cover the top of the table without gaps and overlaps. __________ shape leaves gaps.
__________ triangles cover Table 1.
__________ squares cover Table 3.
__________ rectangles cover Table 4.
The region covered by the triangles, squares or rectangles is called the area of the table.

To find the area of a region, we usually fill it with shapes that tile (no gaps and overlaps), like squares, rectangles and triangles.
Do circles tile? Can we use them to cover a region?
The area of Table 1 is __________ triangle units.
The area of Table 3 is __________ square units.
The area of Table 4 is __________ rectangle units.
Solution:
Yes circle will leave gaps. No, we can’t use them to cover a region.
The area of Table 1 is 0 triangle units.
The area of Table 3 is 8 square units.
The area of Table 4 is 12 rectangle units.

Now, try to cover the top of your table without gaps and overlaps with the following objects of same size.
(a) Notebooks
(b) Lunch boxes
(c) Pencil boxes
(d) Maths textbooks
Which of the above objects covered the region completely?
Solution:
To cover a table without gaps and overlaps with the following objects:
(a) Notebooks
(b) Lunch boxes
(c) Pencil boxes
(d) Maths textbooks

Let Us Do (Page 144)

Look at the different tiles on her desk and answer how many of the following shapes will cover the desk.

(a) Green triangles
(b) Red triangles
(c) Blue squares
Solution:
Total number of squares inside the desk
= 6 × 9 = 54

(a) Green triangle cover half of a square grid Hence, total green tiles required = 54 ÷ \(\frac{1}{2}\)
= 54 × 2
= 108 tiles

(b) Red triangle cover 3 halves + 3 full squares = 4 Hence, total red tiles required = 54 ÷ 4 \(\frac{1}{2}\)
= 54 ÷ \(\frac{9}{2}\)
= 54 × \(\frac{2}{9}\)
= 12 tiles

(c) Blue square cover one full square Hence, total blue tiles required = 54 tiles

Let Us Do (Pages 145-147)

Question 1.
Compare the areas of the two gardens given below on the square grid. Share your observations.
Area of Garden A = __________ cm square
Area of Garden B = __________ cm square

Solution:
Area of Garden A
= 2 cm × 5 cm
= 10 cm squares

Area of Garden B
= 4 cm × 3 cm
= 12 cm squares

Question 2.
Trace your palm on the square grid given below and find the approximate area of your palm. Compare the area of your palm with your friend’s palm. Who has a bigger palm?

Solution:
Try it Yourself.

Question 3.
Collect leaves of different kinds. Put them on a square grid and find their area.
(a) Name the leaf with the largest area.
(b) Name the leaf with the smallest area.
Solution:
Try it yourself

Question 4.
The following mats are made of square patches of equal size. How many square patches will be required to cover each mat? Would both mats require an equal or different number of patches? Trace and cut out a small square of the size give below and find the area.

Area = __________
Perimeter = __________
Solution:
10 square patches
Area = 10 square units (5 × 2 = 10)
Perimeter = 14 units (5+ 2 + 5 + 2 = 14)

Area = __________
Perimeter = __________
Solution:
12 square patches
Area = 12 square units (4 × 3 = 12)
Perimeter = 14 units (4 + 3 + 4 + 3 = 14)
Both mats requires of different square patches.
Area is different but perimeter remains equal.

Trisha makes these two rectangles. She says, “I increased the area of my rectangle, and the perimeter increased.” Do you think this is always true?

Solution:
Increasing area of a figure without increasing the perimeter is not always correct.

Let Us Explore (Pages 147-148)

Question 1.
Tick the shapes with the same area. Find the perimeters of these shapes. What do you notice? Discuss.

Solution:
(a) Area = 6 × 2 = 12 cm²
Perimeter = 2(2 + 6) = 16 cm

(b) Irregular shape. Count the number of square patches
Area = 12 square patches
= 12 cm²

Perimeter = {2(2 + 5) + 5} – 1
= (14 + 5) – 1
= 18 cm

(c) Area = 3 × 4
= 12 cm²
Perimeter = 2(3 + 4)
= 14 cm

(d) Area = 4 × 3
= 12 cm²
Perimeter = 2(4 + 3)
= 14 cm
Area and perimeter of figure (c) and (d) are equal.

(e) Area = 1 × 8
= 8 cm²

Perimeter = 2(8 + 1)
= 18 cm

(f) Area = (12 × 1)
= 12 cm²

Perimeter = 2(12 + 1)
= 26 cm

Area and perimeter of figure (e) and (f) are different. Area of figure (a), (b), (c), (d) and (f) are same.

Question 2.
Tick the shapes with the same perimeter. Find the these shapes. What do you notice? Discuss.

Solution:
(a) Perimeter = {2 × (3 + 2) + 3} – 1
= 12 cm
Area = 7 cm²

(b) Perimeter = {2 × (2 + 3) + 3} – 1
= 12 cm
Area = 7 cm²

(c) Perimeter = (3 × 4) + 2 × (1 + 2) – 2
= 16 cm
Area = 7 cm²

(d) Perimeter = 16 cm
Area = 7 cm²

(e) Perimeter = 2 × (7 + 1)
= 16 cm
Area = 7 cm²

Let Us Do (Pages 149-150)

Question 1.
Draw different shapes having the same area as the given shape. Write the perimeter of each shape. What do you notice? Discuss.

Solution:
Try it yourself.

Question 2.
Is the area of shape (a) less than the area of shape (b) given below? Discuss.

Preetha and Adrit’s grandmother is making another square patchwork. She arranges the patches as shown below. Can you guess how many patches she will need? How did you find it?
Solution:
(a) Area = 3 × 3
= 9 square units

(b) Area = 2(\(\frac{1}{2}\) × 3 × 3)
= 9 square units

Count number of square patches

Area of both shape remains equal.

Let Us Do (Pages 151-153)

Question 1.
Find the area of your classroom floor in square meters. Take the help of your teacher to measure the length and breadth of the floor. What is the perimeter of the classroom floor?
Solution:
Classroom looks like a rectangle.

Length = 20 m
Breadth = 15 m
Perimeter of a classroom = Sum of all the sides
= (20 + 15 + 20 + 15) m
= (2 × 20) + (2 × 15) m
= 70 m

Question 2.
Find the area and perimeter of the following shapes.

Solution:
We can use the formula for finding the Area and Perimeter.
Area of a square = (side × side) unit²
Perimeter of a square = (4 × side) unit
Area of a rectangle = (length × breadth) unit²
Perimeter of a rectangle = 2 × length + 2 × breadth

(a) Square: Side = 6 cm
Area = side × side
= (6 × 6) cm²
= 36 cm²

Perimeter = 4 × side
= 4 × 6 cm
= 24 cm

(b) Rectangle: Length = 4 cm
and Breadth = 7 cm

Area = length × breadth
= 4 × 7 cm²
= 28 cm²

Perimeter = 2 × length + 2 × breadth
= (2 × 4) + (2 × 7) cm
= 8 + 14
= 22 cm

(c) Rectangle: Length = 12 cm and breadth = 4 cm
Area = length × breadth
= (12 × 4) cm²
= 48 cm²

Perimeter = (2 × length) + (2 × breadth)
= (2 × 12) + (2 × 4) cm
= (24 + 8) cm
= 32 cm

(d) Square: Side = 3 cm
Area = 3 × 3 cm²
= 9 cm²
Perimeter = (4 × 3) cm
= 12 cm

(e) Rectangle: Length = 6 cm
and breadth = 5 cm
Area = (6 × 5) cm²
= 30 cm²
Perimeter = (2 × 6) + (2 × 5) cm
= 12 + 10
= 22 cm

Question 3.
Find the area and perimeter of the following objects. Use a scale or measuring tape to find the length and the breadth of each of the objects.

Solution:

Name of the objects	Area	Perimeter
1. Cover of the Notebook	length × breadth	2 × (l + b)
2. Newspaper	length × breadth	2 × (l + b)
3. Blackboard	length × breadth	2 × (l + b)
4. Ludo board	side × side	4 × side
5.
6.

Notebook
l = 20 cm; b = 10 cm
Area = l × b
= 20 × 10
= 200 cm²

Perimeter = 2 × (20 + 10)
= 2 × 30
= 60 cm

Newspaper
l = 55 cm; b = 35 cm
Area = l × b
= 55 × 35 cm²
= 1925 cm²

Perimeter = 2 × (55 + 35)
= 2 × (90)
= 180 cm

Blackboard
l = 90 cm; b = 60 cm
Area = l × b
= 90 × 60
= 5400 cm²

Perimeter = 2 × (l + b)
= 2 × (90 + 60)
= 300 cm

Ludo board
Side = 30 cm
Area = side × side
= 30 × 30 cm²
= 900 cm²

Perimeter = 4 × 30
= 120 cm

Question 4.
Find the area of a rectangular field whose length is 42 m and breadth is 34 m.
Solution:

Length = 42 m and Breadth = 34 m
Area = ?
Area of a rectangular field = length × breadth
= 42 × 34 m²
= 1428 m²

Question 5.
The area of a rectangular garden is 64 square m and its length is 16 m. What is its breadth?
Solution:
Area of rectangular garden = 64 m²
length = 16 m and breadth = ?
Area of a rectangular garden = length × breadth
16 m × breadth
= 64 m²
breadth = 64 m² ÷ 16 m
breadth = 4 m

Question 6.
Find the area of the following fiure with the dimensions as marked in the fiure

Solution:
Given:
Length = 32 cm and
Breadth = 12 cm + 6 cm = 18 cm
Area of the rectangular figure
= Length × Breadth
= 32 cm × 18 cm
= 576 cm²
Or

Figure I
Length = 32 cm
breadth = 6 cm
Area of figure I = l × b
= 32 × 6
= 196 cm²

Figure II
Length = 32 cm
breadth = 12 cm
Area of figure I = l × b
= 32 × 12
= 384 cm²

Total Area = Area of fig I + Area of fig II
= 192 + 384
= 576 cm²

Let Us Ploy (Page 154)

Question 1.
Take some square tiles and a die and play the game in pairs.

Solution:
Try with your friend in the class.

Question 2.
Roll the die and pick the number of tiles equal to the dots on the die. Arrange them to make a shape or figure.

Solution:
Step I → Roll the die
Pick and place tiles equal to the number appear on the die.
Repeat 3 or 4 times.
Repeat the process.
Finally arrange it and find the perimeter.

Question 3.
Find the perimeter of the tiles.

Solution:
Perimeter =1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
= 10 units

Question 4.
Do not move the tiles. The second player can take turn and add tiles to the same tiled figure.

Solution:
Player 2
Roll the die and add new tiles to existing shape and find perimeter.

Question 5.
Take turns and add tiles to the same figure till the perimeter becomes 24.

The one who makes the perimeter 24 wins the game.

Solution:
Play with your friends.