NCERT Class 5 Maths · Chapter 11

Grandmother’s Quilt

Perimeter (the border) and area (the space inside), with square grids, tiles, and the easy formulas for rectangles and squares.

📌 What you’ll learn in this chapter
  • Perimeter: the total length of the boundary
  • Area: the space a shape covers, measured in square units
  • Finding area by counting squares on a grid
  • Why shapes with the same area can have different perimeters (and the other way round)
  • Formulas: area = length × breadth, perimeter = 2 × (length + breadth)

🧵 Let’s Begin: Border and Inside

Dadi is stitching a patchwork chaddar for Tanvi. First, she wants to sew a golden lace around the edge. How much lace does she need? That’s the perimeter.

Then she wonders how many square patches will fill the whole chaddar. That’s the area.

📏 Part 1: Perimeter

Perimeter = add up the lengths of all the sides.

A photo frame is 20 cm long and 15 cm wide.
Perimeter = 20 + 15 + 20 + 15 = 70 cm

A regular hexagon has 6 equal sides of 4 cm. Perimeter = 6 × 4 = 24 cm

💡 Shortcuts Rectangle: Perimeter = 2 × (length + breadth)
Square: Perimeter = 4 × side
Any shape with equal sides: number of sides × side length

🟩 Part 2: Area

Area is the amount of surface a shape covers. To measure it, we cover the shape with equal tiles without gaps or overlaps.

Circles leave gaps, so they are not good for measuring area. Squares are best! A square with 1 cm sides has an area of 1 square cm (1 sq cm).

Counting squares on a grid

Draw your shape on 1 cm squared paper and count the squares inside. For uneven shapes like a leaf or your palm:

  • Count every full square as 1.
  • Count a square that is half or more covered as 1.
  • Ignore squares that are less than half covered.

This gives an approximate (close) area.

The quick way for rectangles

A rectangle on the grid is made of rows of squares. Instead of counting one by one, multiply!

A carrom board patch is 5 squares long and 3 squares wide → 3 rows of 5 = 15 sq units

💡 Formulas Area of rectangle = length × breadth
Area of square = side × side

🔀 Part 3: Same Area, Different Perimeter

Take 12 square tiles and arrange them as rectangles in different ways:

RectangleAreaPerimeter
12 × 112 sq units26 units
6 × 212 sq units16 units
4 × 312 sq units14 units

The area stays the same, but the perimeter changes! The long thin shape has the biggest perimeter. The “square-like” shape has the smallest.

It also works the other way. A 5 × 1 rectangle and a 3 × 3 square both have perimeter 12, but their areas are 5 and 9.

⚠️ Common mistake “A bigger area always means a bigger perimeter.” ❌
✅ Not always! 10 × 1 has area 10 and perimeter 22, but 4 × 4 has a bigger area (16) and a smaller perimeter (16).

🏠 Part 4: Area of Joined Shapes

For an L-shaped room, split it into two rectangles, find each area, and add.

An L-shaped verandah: one part is 8 m × 3 m, the other part is 4 m × 2 m.
Area = 24 + 8 = 32 sq m

❌ Common Mistakes to Avoid

Mixing up area and perimeter
✅ Perimeter = border (cm). Area = inside (sq cm).
Wrong units
✅ Area is always in square units: sq cm, sq m.
Adding only 2 sides for the perimeter
✅ A rectangle has 4 sides: 2 × (l + b).
Counting grid lines instead of squares
✅ Count the boxes inside.

✏️ Practice Time

Try these on your own first, then check your answer below each question.

Q1. A garden is 25 m long and 12 m wide. Find its perimeter and area.
✅ AnswerPerimeter = 2 × (25 + 12) = 74 m. Area = 25 × 12 = 300 sq m
Q2. A square tile has a side of 9 cm. Find its perimeter and area.
✅ AnswerPerimeter = 4 × 9 = 36 cm. Area = 9 × 9 = 81 sq cm
Q3. A room’s floor has an area of 96 sq m and a length of 12 m. What is its breadth?
✅ Answer96 ÷ 12 = 8 m
Q4. Draw two rectangles with perimeter 20 cm. Do they have the same area?
✅ AnswerFor example, 6 × 4 (area 24) and 8 × 2 (area 16). No, the areas are different.
Q5. How many 2 cm × 2 cm tiles are needed to cover a 10 cm × 8 cm board?
✅ Answer5 tiles along the length × 4 tiles along the breadth = 20 tiles
Q6. Lace costs ₹15 per metre. How much for a border around a 3 m × 2 m tablecloth?
✅ AnswerPerimeter = 10 m. Cost = 10 × 15 = ₹150

📘 NCERT Textbook Activity Help

Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!

Page 142 · Quilt lace

Which lace covers the border?

✅ AnswerCount the patches along the length and the breadth of the quilt. Perimeter = 2 × (length + breadth). Choose the lace that is at least that long. With two laces, split the perimeter, for example one lace for the two long sides and the other for the two short sides.
Let Us Do Q1: Pentagon: 5 × 4 = 20 cm. The 4-sided shape with 5 cm sides: 4 × 5 = 20 cm.
Q2 (sample answers): (a) 26 cm: 8 × 5 or 10 × 3 (b) 18 cm: 5 × 4 or 6 × 3
Page 143 · Rug and tables

Covering the tables

✅ AnswerRug: count the patches in one row and the number of rows, then multiply.
Triangles, squares, and rectangles cover without gaps. Circles leave gaps.
20 triangles cover Table 1 · 8 squares cover Table 3 · 12 rectangles cover Table 4
Area of Table 1 = 20 triangle units · Table 3 = 8 square units · Table 4 = 12 rectangle units
Circles do not tile. Notebooks, pencil boxes, and textbooks (rectangles) can cover the table. Round lunch boxes leave gaps.
Page 144 · Preetha’s desk

How many tiles cover the desk?

✅ AnswerThe desk is 9 × 6 = 54 squares. (a) Each green triangle is half a square → 108 (b) Each red triangle covers 4½ squares → 54 ÷ 4½ = 12 (c) 54 blue squares
Page 145 · Comparing shapes

Rectangles A, B, C and the gardens

✅ AnswerOn the grid: A = 3 × 4 = 12 · B = 2 × 4 = 8 · C = 2 × 5 = 10 squares. A has the largest area. C is bigger than B.
Gardens: Garden A = 10 sq cm · Garden B = 12 sq cm. Garden B is bigger, even though Garden A looks taller.
Page 146 · Palm and leaves

Approximate areas

✅ AnswerThis depends on your own palm and leaves. Count full squares, plus squares that are half or more covered. Big leaves like banana or teak have the largest area. Tulsi or tamarind leaves are among the smallest.
Page 147 · Mats and Trisha

Area and perimeter of mats

✅ AnswerUse the small square as the unit. Mat (a): 5 × 2 → area 10, perimeter 14. Mat (b): 4 × 3 → area 12, perimeter 14. They need a different number of patches, even though the perimeters are the same!
Trisha: Not always true. For example, 10 × 1 (area 10, perimeter 22) → 4 × 4 (area 16, perimeter 16): the area increased but the perimeter decreased.
Pages 147–148 · Let Us Explore

Same area? Same perimeter?

✅ Answer Q1: Same area (12 sq cm): (a), (b), (c), (d), (f). Shape (e) has only 8 squares.
Perimeters: (a) 16 cm · (b) 18 cm · (c) 14 cm · (d) 14 cm · (f) 26 cm. Same area can have different perimeters.
Q2: All five pink shapes have an area of 7 sq cm. Perimeters: (a) 12 · (b) 12 · (c) 16 · (d) 16 · (e) 16. So (a) and (b) have the same perimeter, and (c), (d), and (e) have the same perimeter. Compact shapes have smaller perimeters.
Page 149 · Let Us Do, Q1

Same area, different shapes

✅ AnswerThe given shape is 9 × 2 = 18 sq cm (perimeter 22 cm). Other shapes with area 18: 6 × 3 (perimeter 18) · 18 × 1 (perimeter 38) · an L-shape of 18 squares. The perimeter changes even though the area stays the same.
Page 150 · Shapes (a) and (b), and patchwork

Is (a) smaller than (b)?

✅ AnswerNo, they are equal. Shape (a) = 3 × 3 = 9 squares. Triangle (b) covers half of a 6 × 3 rectangle = 18 ÷ 2 = 9 squares. (You can also pair up the half-squares.) Patchwork: 6 × 4 = 24 patches.
Pages 151–152 · Area and perimeter

Find the area and perimeter

✅ AnswerClassroom: measure it yourself, then area = l × b and perimeter = 2 × (l + b).
(a) 6 cm × 6 cm → area 36 sq cm, perimeter 24 cm
(b) 4 cm × 7 cm → area 28 sq cm, perimeter 22 cm
(c) 12 cm × 4 cm → area 48 sq cm, perimeter 32 cm
(d) 3 cm × 3 cm → area 9 sq cm, perimeter 12 cm
(e) 6 cm × 5 cm → area 30 sq cm, perimeter 22 cm
Page 153 · Q3–Q6

Objects, field, garden, and figure

✅ AnswerQ3: Measure your own objects (e.g. a notebook of 24 cm × 18 cm → area 432 sq cm, perimeter 84 cm).
Q4: 42 × 34 = 1,428 sq m
Q5: 64 ÷ 16 = 4 m
Q6: The whole figure is one rectangle, 32 cm long and 6 + 12 = 18 cm tall. Area = 32 × 18 = 576 sq cm. (The dotted lines only divide it into parts.)
Page 154 · Let Us Play

Perimeter game

✅ AnswerTip to win: adding a tile to the side of a line of tiles increases the perimeter by 2. Adding a tile into a corner “notch” does not change the perimeter. Plan your moves so that you reach exactly 24.

👨‍👩‍👧 Tips for Parents

  • Measure a bed sheet or table with a tape. Find the lace needed (perimeter) and the cloth needed (area).
  • Count floor tiles in a room to find its area in “tile units”.
  • Use 12 coins or blocks to make different rectangles and compare the perimeters.
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