Grandmother’s Quilt NCERT Solutions | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

Page No. 142

Let Us Do

Q1: Find the perimeter of the following shapes. All sides of the following shapes are equal.
Ans:
Perimeter of a shape
= Sum of lengths all sides Perimeter
= (4 + 4 + 4 + 4 + 4) cm
= 20 cm
Perimeter
= (5 + 5 + 5 + 5 + 5 + 5) cm
= 30 cm

Q2: Draw two rectangles each having the following perimeters.
(a) 26 cm
Ans:

(b) 18 cm
Ans:

Page No. 143

Preetha and Adrit’s grandmother is making a rug with square patches. The picture below shows the rug. 
How many patches have they used to make this?

Ans:
They have used 90 square patches to make the rug.

Q: Preetha and Adrit are trying to cover their table with different shapes. Preetha covered it with triangles and circles. Adrit covered with squares and rectangles.
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
Ans:
They found that triangle, square and rectangle shapes cover the top of the table without gaps and overlaps. Circle shape leaves gaps.
20 triangles cover Table 1.
8 squares cover Table 3.
12 rectangles cover Table 4.

Q: 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
Ans:
No, circles do not tile. We cannot use them to cover a region because circles leave gaps.
The area of Table 1 is 20 triangle units.
The area of Table 3 is 8 square units.
The area of Table 4 is 12 rectangle units.

Q: 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?
Ans:
Do it yourself.

Page No. 144

Let Us Do

Preetha is playing with tiles. She covers her desk with different shapes as shown below.
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 _______
Ans:
In the given picture, we can see that the desk is made of 54 squares.
(а) 2 green triangles = 1 square
2 × 54 = 108 green triangles = 54 squares
Therefore, 108 green triangles will cover the desk.

(b) 1 red triangle = squares = 9/2 squares
Since there are 54 squares on the desk. Therefore, required number of red triangles =

Therefore, 12 red triangles will cover the desk.

(c) 1 blue square = 1 square
Therefore, 54 blue squares will cover the desk.

Let Us Do

Q1: 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
Ans:
In the given picture, garden A is covered by 10 unit squares each of side 1 cm.
Therefore, Area of Garden A = 10 cm square In the given picture, garden B is covered by 12 unit squares, each of side 1 cm. Therefore, Area of Garden B = 12 cm square So, the area of Garden B is larger than the area of Garden A.

Q2: 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?
Ans:
Do it yourself.

Q3: 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.
Ans:
Do it yourself.

Q4: 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.
Ans:
Do it yourself.

Q: 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?
Ans:
To increase the area of a given rectangle, we need to add unit squares along its length or breadth or both the dimensions. In each case the length around the edge will increase and hence the perimeter of the rectangle will increase.

No, it is not always true. For example,
Let us take a rectangle whose length = 8 cm and breadth = 1 cm.
Therefore, perimeter of rectangle
= 2(8 + 1) = 18 cm
Area of rectangle = 8 × 1 = 8 sq. cm
Now rearrange the sides of the rectangle as length = 5 cm
and breadth 3 cm Therefore, Perimeter of rectangle = 2(5 + 3)
= 16 cm
Area of the rectangle = 5 × 3
= 15 sq. cm
Hence it is not always true that increase the area of rectangle, its perimeter increases.

Let Us Explore

Q1: Tick the shapes with the same area. Find the perimeters of these shapes. What do you notice? Discuss.

Ans:

(a) Perimeter = 16 cm, Area = 12 cm square
(b) Perimeter = 18 cm; Area = 12 cm square
(c) Perimeter = 14 cm; Area = 12 cm square
(d) Perimeter = 14 cm; Area = 12 cm square
(e) Perimeter = 18 cm; Area = 8 cm square
(f) Perimeter = 26 cm; Area = 12 cm square
Here, area of shapes (a), (b), (c), (d), and (f) is same.
We can see that shapes can have same area but different perimeters.

Q2: Tick the shapes with the same perimeter. Find the areas of these shapes. What do you notice? Discuss.
Ans:
(a) Perimeter = 12 cm; Area = 7 cm square
(b) Perimeter = 12 cm; Area = 7 cm square
(c) Perimeter = 16 cm; Area = 7 cm square
(d) Perimeter = 16 cm; Area = 7 cm square
(e) Perimeter = 16 cm; Area = 7 cm square
Shapes (a) and (b) have same perimeter, and shapes (c), (d), (e) have same perimeter.
We observed that, different shapes can have same area and same perimeter.

Page No. 149-150

Let Us Do

Q1: Draw different shapes having the same area as the given shape. Write the perimeter of each shape. What do you notice? Discuss.
Ans:
(а) Area = 18 cm square; Perimeter = 22 cm
(b) Area = 18 cm square; Perimeter = 18 cm
(c) Area = 18 cm square; Perimeter = 22 cm
(d) Area =18 cm square; Perimeter = 26 cm
Shapes having the same area can have different perimeters. (Answer may vary)

Q2:  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?
Ans:
Area of shape (a) = 9 unit squares
Area of shape (b) = 6 full unit squares + 6 half unit squares = 9 unit squares
So, the area of shape (a) is equal to the area shape (b).

Page No. 151-153

Let Us Do

Q1: 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?
Ans:
Do it yourself.

Q2: Find the area and perimeter of the following shapes.
Ans:
(a) Length of the square = 6 cm
Area = Length × Length
= 6 × 6
= 36 square cm
Perimeter = 4 × Length
= 4 × 6
= 24 cm

(b) Length = 4 cm, Breadth = 7 cm
Area of rectangle = Length × Breadth
= 4 × 7
= 28 square cm 
Perimeter of rectangle
– = 2 × Length + 2 × Breadth
= 2 × 4 + 2 × 7
= 8 + 14
= 22 cm

(c) Length = 12 cm, Breadth = 4 cm
Area of rectangle = Length × Breadth
= 12 × 4
= 48 square cm
Perimeter of rectangle
= 2 × Length + 2 × Breadth
= 2 × 12 + 2 × 4
= 24 + 8
= 32 cm

(d) Length of the square = 3 cm
Area of square = Length × Length
= 3 × 3
= 9 square cm
Perimeter of square = 4 × length
= 4 × 3
= 12 cm

(e) Length = 6 cm, Breadth = 5 cm
Area of rectangle = Length × Breadth = 6 × 5
= 30 square cm
Perimeter of rectangle
= 2 × Length + 2 × Breadth
= 2 × 6 + 2 × 5
= 12 + 10
= 22 cm

Q3: 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.
Ans:
Do it yourself.

Q4: Find the area of a rectangular field whose length is 42 m and breadth is 34 m.
Ans:
Length = 42 m, Breadth = 34 m
Area of rectangle = Length × Breadth
= 42 × 34
= 1428 square m
Therefore, the area of the rectangular field is 1428 square m.

Q5: The area of a rectangular garden is 64 square m and its length is 16 m. What is its breadth?
Ans:
Area = 64 square m, Length = 16m
Area of rectangle = Length × Breadth
64 = 16 × Breadth
Breadth = 64 + 16 = 4 m
Therefore, the breadth of rectangular garden is 4 m.

Q6: Find the area of the following figure with the dimensions as marked in the figure.
Ans:
Length = 32 cm,
Breadth = (6 + 12) cm = 18 cm
Area of the rectangular figure = Length × Breadth
= 32 × 18
= 576 square cm