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NCERT Solutions for Class 5th Maths Chapter 11 Grandmother's square patchwork: Area = Length × Breadth — Area of a Rectangle

Book page 150 Updated on2026-09-19

Q1.
What are other ways of finding area?
Answer

There are three ways, and they get quicker as you go down the list.

  1. Cover and count the tiles. Lay squares over the shape and count them one by one. Slow, but it always works and it shows what area really means.
  2. Put the shape on a square grid and count squares. No tiles needed. Count whole squares first, then the part squares.
  3. For a rectangle, multiply. Count how many squares fit along the length, count how many rows there are, and multiply the two numbers.
Area of a rectangle = Length × Breadth
Why multiplying works: A rectangle drawn on a grid is made of equal rows. If one row holds 6 squares and there are 4 such rows, the total is 6 taken 4 times. That is exactly what 6 × 4 means. So the multiplication is not a new rule — it is just a faster way of doing the same counting.
Careful: Multiplying only works when the shape is a rectangle, so that all the rows are equally full. For a stepped or curved shape you must go back to counting squares.
Q2.
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?
BreadthLength
Grandmother's patchwork. The patches she has already laid are shown in pink.
Answer

She will need 24 patches.

Length 6 patches, breadth 4 patches
Grandmother has laid the top row and the left column. The whole rectangle needs 6 × 4 = 24 patches.
  1. Look at what she has already laid. The top row has 4 patches, so every row will hold 4 patches.
  2. Look at the left column. It has 6 patches, so there will be 6 rows.
  3. Do not count the whole thing. 6 rows of 4 patches each is 6 × 4.
  4. Multiply. 6 × 4 = 24 patches.
Patches in one row = 4
Number of rows = 6
Total patches = 6 × 4 = 24 patches
Area of the patchwork = 6 cm × 4 cm = 24 square cm
Why the two arms are enough: Grandmother has laid one full row and one full column. The row tells us how wide the rectangle is; the column tells us how tall. Every other row will be a copy of the first one, so nothing more needs to be counted.
Check it yourself: Add instead. 4 + 4 + 4 + 4 + 4 + 4 = 24. The same answer, but multiplying was much faster.
Q3.
Did you notice that 6 is the length of one side and 4 is the length of the non-equal side of the rectangle?
Answer

Yes. The 6 we multiplied is the length of the patchwork and the 4 is its breadth.

  1. The number of patches in one row is the same as the number of centimetres along the long side. Here, 6.
  2. The number of rows is the same as the number of centimetres along the short side. Here, 4.
  3. So “rows × patches in a row” is really “length × breadth”.
Rows × patches in a row = 6 × 4 = 24 patches
Length × Breadth = 6 cm × 4 cm = 24 square cm
Same numbers, same answer
Why the two ways match: Each patch is 1 cm wide. So laying 6 patches in a row makes a row 6 cm long, and stacking 4 rows makes the patchwork 4 cm tall. Counting patches and measuring with a ruler must therefore give the same numbers.
New words: the length is the longer side of a rectangle and the breadth is the shorter side. The book calls the breadth “the non-equal side” because it is not equal to the length.
Q4.
Go back to the previous examples and check whether the product of the length and the breadth of the rectangles is the same as the area you had calculated by counting.
Answer

Yes — in every rectangle in this chapter, length × breadth gives exactly the area we had counted.

RectangleArea by countingLength × BreadthMatch?
Table 3 (page 143)8 square units4 × 2 = 8✓
Rectangle A (page 145)12 unit squares3 × 4 = 12✓
Rectangle B (page 145)8 unit squares2 × 4 = 8✓
Rectangle C (page 145)10 unit squares2 × 5 = 10✓
Garden A (page 145)10 square cm2 × 5 = 10✓
Garden B (page 145)12 square cm4 × 3 = 12✓
Mat (a) (page 147)10 patches5 × 2 = 10✓
Mat (b) (page 147)12 patches4 × 3 = 12✓
Shape (a) (page 149)18 square cm9 × 2 = 18✓
Why it always matches: Multiplying is only a short cut for counting equal rows. Since every rectangle on a grid is made of equal rows, the short cut can never give a different answer from the slow count.
Remember: Area of a rectangle = Length × Breadth. Count squares when you need to be sure; multiply when you want to be quick.
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