NCERT Solutions for Class 5th Maths Chapter 11 Rectangles A, B and C — Comparing Shapes
Book page 144–145 Updated on2026-09-19
Q1.
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.
Three rectangles cut from coloured paper.
Answer
Rectangle A has the largest area.
Here is how to find out with paper and scissors, the way the book asks.
Trace all three rectangles on a sheet of paper and cut them out neatly.
Put A on top of B. B disappears completely under A, and some of A still shows. So A is bigger than B.
Put A on top of C. C is narrow but tall, so it pokes out at the bottom while A pokes out at the side. Neither hides the other, so we cannot tell yet.
Cut and rearrange. Cut the bit of C that pokes out and slide it beside the rest. Now C fits inside A with a little of A left over. So A is the largest.
Why cutting is needed: Covering one shape with another only settles the question when one hides the other completely. When each one pokes out somewhere, the eye cannot judge. Cutting and rearranging turns both into the same kind of shape so they can be compared.
Coming next: On page 145 the book gives us a much easier tool — a square grid. Then we simply count squares and no cutting is needed at all.
Q2.
Do you see that the area of rectangle A is larger than that of B? What about B and C?
Answer
Yes, A is larger than B. And C is larger than B. So the order so far is A and C both above B.
Count the squares: A = 12, B = 8, C = 10.
Area of A = 3 × 4 = 12 unit squares Area of B = 2 × 4 = 8 unit squares Area of C = 2 × 5 = 10 unit squares
A and B. Both are 4 squares tall, but A is 3 squares wide while B is only 2 squares wide. Same height, more width, so A > B.
B and C. Both are 2 squares wide, but C is 5 squares tall while B is only 4. Same width, more height, so C > B.
Why you can compare these two pairs by eye: In each pair one measurement is the same. When only one measurement changes, the bigger one is easy to see. It is only when both measurements change — as with A and C — that the eye gets stuck.
Q3.
Which shape has a larger area among A and C? How will you find out?
Answer
A has the larger area. A covers 12 unit squares and C covers 10 unit squares.
Here are two ways to find out.
Way 1 — cut and fit. Trace both, cut them out, then cut C into pieces and try to lay those pieces inside A. They all fit, and 2 squares of A are still empty. So A is bigger.
Way 2 — use a square grid. Place both rectangles on the same square grid and count the squares each one covers. A covers 12, C covers 10.
A is 3 squares wide and 4 squares tall → 3 × 4 = 12 C is 2 squares wide and 5 squares tall → 2 × 5 = 10 12 > 10, so A is larger
Why A wins even though C is taller: C is taller by 1 square but narrower by 1 square. Losing a whole column of 4 squares costs more than gaining a short row of 2 squares. Area depends on both measurements together, not on height alone.
The order: A (12) > C (10) > B (8).
Q4.
Let us put these rectangles on a square grid. Now, can you identify the rectangle that has the largest area?
Answer
Yes — rectangle A, with an area of 12 unit squares.
A = 12, B = 8, C = 10 unit squares. A is the largest.
Look at A. 3 squares across, 4 rows down. 3 × 4 = 12 unit squares.
Look at B. 2 squares across, 4 rows down. 2 × 4 = 8 unit squares.
Look at C. 2 squares across, 5 rows down. 2 × 5 = 10 unit squares.
Compare. 12 is the biggest, so A has the largest area.
A = 12 unit squares · B = 8 unit squares · C = 10 unit squares A has the largest area.
Why the grid makes this so easy: All the squares of the grid are exactly the same size. So the shape that covers more squares must cover more surface. There is nothing to judge by eye and nothing to cut. This is why the book says a square grid is the most convenient way to find area. A square with sides of 1 unit has an area of 1 unit square.
New word:unit square — one little square of the grid, the amount of surface we count with. When the grid squares are 1 cm across, one unit square is 1 square cm.