NCERT Solutions Class 5 Mathematics Mela Chapter 11 Grandmothers Quilt

Page 142

Question. Preetha and Adrit's grandmother made a quilt cover using old clothes. Now she wants to decorate it with lace. Tick the lace option that would cover the entire border of the quilt. She decides to use two different coloured laces. How much lace of each kind will be needed to cover the entire border?
Answer: By counting the small equal units (squares) along the border, the quilt measures 15 units on the top side, 15 units on the bottom side, 10 units on the left side, and 10 units on the right side. The total distance around the quilt's edge (perimeter) equals 15 + 15 + 10 + 10 = 50 units. The available lace options are: Red lace = 40 units, Green lace = 50 units, Blue lace = 25 units. Since she wants to use two different colours and divide the border equally, she splits 50 ÷ 2 = 25 units for each colour. Among the available options, the blue lace measures exactly 25 units. Therefore, she can use blue lace for 25 units and half of the green roll (which is 25 units) to complete the border.
In simple words: Add up all four sides of the quilt to get the total border length. Then divide this by 2 to find how much of each colour is needed.

Exam Tip: Always count the grid squares carefully along each edge and remember that the perimeter is the sum of all four sides.

Question 1. Find the perimeter of the following shapes. All sides of the following shapes are equal.
Answer: The perimeter is the total length around any shape. To find it, multiply the number of sides by the length of one side. The first shape is a pentagon with 5 sides, each measuring 4 cm long. Using the formula: Perimeter = 5 × 4 = 20 cm. The second shape consists of joined triangles with 6 equal sides in total. Each side measures 5 cm. Using the same method: Perimeter = 6 × 5 = 30 cm.
In simple words: Count how many sides the shape has. Multiply this number by how long one side is.

Exam Tip: Make sure all sides are truly equal before using this method, and always double-check your counting of the total number of sides.

Question 2. Draw two rectangles each having the following perimeters. (a) 26 cm (b) 18 cm
Answer: For a rectangle with perimeter 26 cm: one possible rectangle is 10 cm long and 3 cm wide. Check: 2 × (10 + 3) = 26 cm. For a rectangle with perimeter 18 cm: one possible rectangle is 6 cm long and 3 cm wide. Check: 2 × (6 + 3) = 18 cm. Both rectangles can be drawn on paper using these measurements.
In simple words: Use the formula perimeter = 2 × (length + width) to find dimensions that work, then sketch the rectangles.

Exam Tip: Remember there are multiple correct answers - any length and width that add up to half the perimeter will work.

Question. 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?
Answer: A row runs across the rug from left to right, and this rug contains 6 rows. A column runs up and down the rug from top to bottom, and this rug contains 15 columns. To find the total patches, use the formula: Total Patches = Number of Rows × Number of Columns. Therefore: Total Patches = 6 × 15 = 90. Preetha and Adrit's grandmother used 90 patches to make the rug.
In simple words: Count the rows and columns, then multiply them together to find the total number of patches.

Exam Tip: Always clarify the difference between rows (horizontal lines) and columns (vertical lines) to avoid mistakes in your counting.

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.

Question. 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.
Answer: Triangles, squares, and rectangles are the shapes that cover the top of the table without gaps and overlaps. The circle shape leaves gaps. 20 triangles cover Table 1. 8 squares cover Table 3. 6 rectangles cover Table 4.
In simple words: Some shapes fit together perfectly with no empty spaces, while circular shapes cannot because their curved edges create gaps.

Exam Tip: When counting shapes on a grid, count systematically row by row to avoid missing any or counting twice.

Question. 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.
Answer: Circles do not tile because their rounded edges create empty spaces between them, and proper tiling requires covering a surface completely with no holes. Table 2 shows this clearly - when circles are used, gaps remain between the circles and at the edges. Tiling means filling a region with no gaps and no overlaps. The area of Table 1 equals 20 triangle units. The area of Table 3 equals 8 square units. The area of Table 4 equals 12 rectangle units.
In simple words: Shapes with straight edges fit together perfectly, but circular shapes leave holes, so they cannot be used for tiling.

Exam Tip: Understand that tiling is only possible with shapes that have straight edges and can fit together with no gaps.

Let Us Do on Page 144

Question. 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 __________
Answer: (a) Green triangles = 18
(b) Red triangles = 6
(c) Blue squares = 18
In simple words: Count each type of shape carefully by going through the desk area in an organized way, row by row.

Exam Tip: Organize your counting method systematically to ensure accuracy and avoid recounting the same tiles.

Comparing Shapes

Question. Which of the above rectangles has the largest area? Trace these shapes on to a paper and cut them to find out the one that has the largest area. Do you see that the area of rectangle A is larger than that of B? What about B and C?
Answer: Rectangle A (Yellow) covers 4 rows and 3 columns, giving an area of 4 × 3 = 12 unit squares. Rectangle B (Pink) covers 4 rows and 2 columns, giving an area of 4 × 2 = 8 unit squares. Rectangle C (Purple) covers 5 rows and 2 columns, giving an area of 5 × 2 = 10 unit squares. Therefore, rectangle A has the largest area. When comparing B and C, rectangle C is larger than rectangle B.
In simple words: Multiply the rows by the columns to find each shape's area, then compare the numbers to determine which is biggest.

Exam Tip: Always count rows and columns separately, then multiply to find the area - this method works for any rectangle.

Let Us Do on Page 145

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.
Answer: Garden A measures 2 columns wide and 5 rows tall. Its area = 2 × 5 = 10 cm square. Garden B measures 4 columns wide and 3 rows tall. Its area = 4 × 3 = 12 cm square. Garden B has a larger area than Garden A.
In simple words: Count how many columns and rows each garden covers, multiply them, and compare the results.

Exam Tip: Use the grid to help you count accurately, and always show your multiplication to demonstrate your thinking.

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?
Answer: When tracing a palm on a grid, count the full squares covered and add up partial squares. For example, one palm might cover approximately 27 square units, while a friend's palm covers about 26 square units. By comparing the counts, you can determine whose palm is bigger. In this example, the first palm is slightly larger than the friend's palm.
In simple words: Trace your hand outline, count the squares inside it, and compare your count with your friend's count.

Exam Tip: When counting partial squares, use the rule that two half-squares equal one full square to make your counting more accurate.

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.
Answer: Different leaves have varying areas based on their shape and size. Examples include: a mango leaf (long and narrow, approximately 78 square units), a peepal leaf (heart-shaped, approximately 44 square units), a neem leaflet (small and serrated, approximately 15 square units), tulsi leaves (small ovals in a cluster, approximately 9 square units), a maple leaf (broad with pointed lobes, approximately 73 square units), and a curry leaf (thin and long, approximately 47 square units). Comparing these measurements, the mango leaf has the largest area at 78 square units, while tulsi leaves have the smallest area at 9 square units.
In simple words: Lay each leaf on a grid, count the squares it covers, and write down the numbers so you can find the biggest and smallest.

Exam Tip: Be consistent in your counting method for all leaves so the comparison is fair and accurate.

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 given below and find the area.
Answer: (a) Counting the patches along the length and width: Length = 5 patches, Width = 2 patches. Total patches = 5 × 2 = 10 patches. Area of mat (a) = 10 square units. Perimeter of mat (a) = 2 × (5 + 2) = 14 units.
(b) Counting the patches along the length and width: Length = 4 patches, Width = 3 patches. Total patches = 4 × 3 = 12 patches. Area of mat (b) = 12 square units. Perimeter of mat (b) = 2 × (4 + 3) = 14 units. The two mats require different numbers of patches (10 and 12), so the answer is that they need different amounts.
In simple words: Multiply the length patches by the width patches to find how many patches cover each mat.

Exam Tip: Remember the difference between area (number of patches covering a surface) and perimeter (distance around the edge).

Question. 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?
Answer: Looking at Trisha's first (smaller) rectangle: it is 2 blocks wide and 3 blocks tall, giving a total area of 2 × 3 = 6 square units. Its perimeter = 2 × (3 + 2) = 10 units. Her second (larger) rectangle is 3 blocks wide and 4 blocks tall, with an area of 3 × 4 = 12 square units. Its perimeter = 2 × (4 + 3) = 14 units. In this case, the area increased from 6 to 12 square units, and the perimeter also increased from 10 to 14 units, so Trisha's statement appears true. However, this is not always true. Consider Rectangle A with length 6 and width 1: Area = 6 × 1 = 6 square units, Perimeter = 2 × (6 + 1) = 14 units. Now Rectangle B with length 4 and width 3: Area = 4 × 3 = 12 square units, Perimeter = 2 × (4 + 3) = 14 units. Here, the area increased from 6 to 12 square units, but the perimeter stayed the same at 14 units. This proves that increasing area does not always lead to an increase in perimeter.
In simple words: Sometimes when a shape gets bigger, its border gets longer. But sometimes it can get bigger without the border getting longer - it depends on the shape.

Exam Tip: Always test with multiple examples before deciding if a statement is always true or sometimes false - one counterexample is enough to disprove a rule.

Let Us Explore on Page 147

Question 1. Tick the shapes with the same area. Find the perimeters of these shapes. What do you notice? Discuss.
Answer: (a) Length = 6 units, Width = 2 units. Area = 6 × 2 = 12 square units. Perimeter = 2 × (6 + 2) = 16 units.
(b) Length = 2 units, Width = 6 units. Area = 2 × 6 = 12 square units. Perimeter = 2 × (2 + 6) = 16 units.
(c) Length = 3 units, Width = 4 units. Area = 3 × 4 = 12 square units. Perimeter = 2 × (3 + 4) = 14 units.
(d) Length = 4 units, Width = 3 units. Area = 4 × 3 = 12 square units. Perimeter = 2 × (4 + 3) = 14 units.
(e) Length = 8 units, Width = 1 unit. Area = 8 × 1 = 8 square units. Perimeter = 2 × (8 + 1) = 18 units.
(f) Length = 12 units, Width = 1 unit. Area = 12 × 1 = 12 square units. Perimeter = 2 × (12 + 1) = 26 units.
Shapes a, b, c, and d all have the same area of 12 square units. However, their perimeters are different - shapes a and b both have a perimeter of 16 units, while shapes c and d both have a perimeter of 14 units. Shape f also has an area of 12 square units but a perimeter of 26 units. This shows that shapes can have identical areas but different perimeters.
In simple words: Multiple rectangles can cover the same amount of space (same area) but have different distances around their edges (different perimeters).

Exam Tip: Recognize that area and perimeter are independent properties - knowing one does not tell you the other.

Question 2. Tick the shapes with the same perimeter. Find the areas of these shapes. What do you notice? Discuss.
Answer: Examining the given shapes: shapes c and d both have a perimeter of 14 units but different areas. Shape c has an area of 12 square units, while shape d also has an area of 12 square units, so they have the same area. When we look at other shapes with a perimeter of 14 units, they may have different areas depending on their length and width. For instance, a rectangle that is 5 units long and 2 units wide has a perimeter of 2 × (5 + 2) = 14 units and an area of 5 × 2 = 10 square units. A rectangle that is 4 units long and 3 units wide has a perimeter of 2 × (4 + 3) = 14 units and an area of 4 × 3 = 12 square units. This demonstrates that shapes can share the same perimeter while having different areas. The key observation is that as a rectangle becomes more elongated (one very long side and one very short side), its area decreases while its perimeter may remain constant or increase slightly depending on the dimensions.
In simple words: Shapes that have the same border distance (perimeter) can cover different amounts of space (different areas).

Exam Tip: Always calculate both area and perimeter separately - one does not determine the other, so test multiple examples to see the relationship.

Page 149

Let Us Do

Question 1. Draw different shapes having the same area as the given shape. Write the perimeter of each shape. What do you notice? Discuss.
Answer: The five shapes (a), (b), (c), (d), and (e) all have an area of 7 square units. However, their perimeters differ - shapes (a) and (b) each have a perimeter of 12 units, while shapes (c), (d), and (e) each have a perimeter of 16 units. Even though these shapes are arranged in different ways, they cover the same amount of space. This shows that different shapes can enclose the same area but have different outer boundaries.
In simple words: All these shapes take up the same space (7 square units), but some have shorter boundaries and some have longer boundaries. The shape you make changes how far you walk around it, even if the space inside stays the same.

Exam Tip: When comparing shapes by area and perimeter, always count the grid squares carefully for area and trace the outer edge completely for perimeter - do not skip any edge, especially where the shape is jagged or uneven.

Question 2. Look at the following shapes and find their perimeters. What do you notice?
Answer: When you measure the perimeters of the six shapes shown, you get:
(a) 22 units
(b) 26 units
(c) 20 units
(d) 38 units
(e) 38 units
(f) 38 units

Even though all these shapes cover the same area, their perimeters are not all the same. The way each shape is arranged - how stretched out or compact it is - changes its perimeter. This happens because turning the shape or rearranging how it looks on the grid changes the outer boundary, even if the amount of space covered stays equal.
In simple words: The shape's form matters for perimeter. Two shapes with the same area can have very different distances around them.

Exam Tip: Remember that area and perimeter are independent - knowing the area does not tell you the perimeter, and knowing the perimeter does not tell you the area. Always calculate both separately.

Question 3. Is the area of shape (a) less than the area of shape (b) given below? Discuss. What are the other ways of finding area?
Answer: No, the area of shape (a) is not less than the area of shape (b). Both shapes occupy exactly the same area. When you count the grid squares in shape (a), you get 9 unit squares. Shape (b) also covers 9 unit squares. Although the two shapes look very different from each other, they enclose equal amounts of space. Therefore, the area of shape (a) equals the area of shape (b).

Other ways to find area include:
- Counting unit squares on a grid
- Using the formula Area = Length × Breadth for rectangles
- Breaking an irregular shape into smaller rectangles, finding each rectangle's area, then adding them together
- Using multiplication when the shape forms regular rows and columns
In simple words: Different shapes can hold the same space inside even if they do not look alike. You can count squares, use a formula, or break the shape into smaller pieces to find how much space it takes up.

Exam Tip: For composite shapes (shapes made of multiple rectangles), always break them into individual rectangles first, calculate each area, then add them - this method avoids mistakes.

Question. Can you guess how many patches Preetha and Adrit's grandmother will need? How did you find it?
Answer: The grandmother will need 15 patches for her patchwork square. Instead of counting each patch individually, you can use multiplication to find the answer more quickly. The arrangement has 5 rows, with 3 patches in each row. So you multiply: 5 × 3 = 15 patches. This method of using rows and columns saves time and is less likely to result in a counting mistake.
In simple words: You do not have to count one by one. Count how many rows you have and how many patches are in each row, then multiply them together.

Exam Tip: Using the "rows and columns" multiplication method works for any rectangular grid of objects - it is faster and more reliable than counting each item individually.

Page 151

Let Us Do

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?
Answer: With my teacher's assistance, I measured my classroom floor and found:

Length of the classroom = 8 meters
Breadth of the classroom = 6 meters

To find the area, I used the formula:
Area = Length × Breadth
Area = 8 × 6 = 48 square meters

So the area of my classroom floor is 48 square meters.

To find the perimeter, I used the formula:
Perimeter = 2 × (Length + Breadth)
Perimeter = 2 × (8 + 6)
Perimeter = 2 × 14 = 28 meters

So the perimeter of my classroom floor is 28 meters.
In simple words: Multiply length and breadth to get area. Add length and breadth, then multiply by 2 to get the distance all the way around the floor.

Exam Tip: Always state your measurements first, then show the formula, then substitute the values, and finally write the answer with the correct unit (square meters for area, meters for perimeter).

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

(a) Length = 6 cm, Width = 6 cm
Area = 6 × 6 = 36 cm²
Perimeter = 2 × (6 + 6) = 2 × 12 = 24 cm

(b) Length = 7 cm, Width = 4 cm
Area = 7 × 4 = 28 cm²
Perimeter = 2 × (7 + 4) = 2 × 11 = 22 cm

(c) Length = 12 cm, Width = 4 cm
Area = 12 × 4 = 48 cm²
Perimeter = 2 × (12 + 4) = 2 × 16 = 32 cm

(d) Length = 3 cm, Width = 3 cm
Area = 3 × 3 = 9 cm²
Perimeter = 2 × (3 + 3) = 2 × 6 = 12 cm

(e) Length = 6 cm, Width = 5 cm
Area = 6 × 5 = 30 cm²
Perimeter = 2 × (6 + 5) = 2 × 11 = 22 cm
In simple words: For each shape, multiply the two sides to get area, then add the two sides and multiply by 2 to get perimeter.

Exam Tip: Keep your working organized with clear labels - write the length and width first, then show the formula applied to those numbers, then give the final answer with units.

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.
Answer:

Cover of the Notebook: Length = 0.30 m, Breadth = 0.20 m
Area = 0.30 × 0.20 = 0.06 sq m
Perimeter = 2 × (0.30 + 0.20) = 1.00 m

Newspaper: Length = 0.60 m, Breadth = 0.40 m
Area = 0.60 × 0.40 = 0.24 sq m
Perimeter = 2 × (0.60 + 0.40) = 2.00 m

Blackboard: Length = 2.00 m, Breadth = 1.20 m
Area = 2.00 × 1.20 = 2.40 sq m
Perimeter = 2 × (2.00 + 1.20) = 6.40 m

Ludo Board: Length = 0.45 m, Breadth = 0.45 m
Area = 0.45 × 0.45 = 0.2025 sq m
Perimeter = 2 × (0.45 + 0.45) = 1.80 m

My Study Table: Length = 1.20 m, Breadth = 0.60 m
Area = 1.20 × 0.60 = 0.72 sq m
Perimeter = 2 × (1.20 + 0.60) = 3.60 m

Bedsheet: Length = 2.00 m, Breadth = 1.50 m
Area = 2.00 × 1.50 = 3.00 sq m
Perimeter = 2 × (2.00 + 1.50) = 7.00 m
In simple words: Measure each object with a tape. Write down the length and width in meters. Then multiply them for area, and add them and multiply by 2 for perimeter.

Exam Tip: When measuring real objects, convert all measurements to the same unit before calculating - if using meters, make sure all dimensions are in meters, not a mix of meters and centimeters.

Question 4. Find the area of a rectangular field whose length is 42 m and breadth is 34 m.
Answer: Given:
Length = 42 m
Breadth = 34 m

Using the formula Area = Length × Breadth:
Area = 42 × 34 = 1,428 square meters

The rectangular field covers an area of 1,428 square meters.
In simple words: Multiply the two measurements together to find how much space the field takes up.

Exam Tip: Always write "Given" at the start, state the formula you are using, show the multiplication, and give the final answer with the correct unit (square meters).

Question 5. The area of a rectangular garden is 64 square m and its length is 16 m. What is its breadth?
Answer: Given:
Area = 64 square meters
Length = 16 meters

Using the formula Area = Length × Breadth, I can rearrange it to find breadth:
Breadth = Area ÷ Length
Breadth = 64 ÷ 16
Breadth = 4 meters

The breadth of the rectangular garden is 4 meters.
In simple words: When you know the area and one side, divide the area by that side to find the other side.

Exam Tip: This type of problem requires you to rearrange the formula - if Area = Length × Breadth, then Breadth = Area ÷ Length - remember to divide, not multiply.

Question 6. Find the area of the following figure with the dimensions as marked in the figure.
Answer: From the figure, I can identify:
Total Length = 32 cm

The total width on the left side is made up of two sections:
- Top section = 6 cm
- Bottom section = 12 cm
Total Width = 6 + 12 = 18 cm

Using the formula Area = Length × Width:
Area = 32 × 18 = 576 square cm

The area of the figure is 576 square cm.
In simple words: Add up the two width measurements on the left side to get the full width, then multiply it by the length at the top.

Exam Tip: For composite figures with stacked or joined sections, always find the total length and total width by adding the marked segments before multiplying - do not try to multiply partial dimensions.