Let us find the perimeter of some shapes using the dot grid. One is done for you. A B C D E 10 cm The five shapes on the dot grid on page 92. Every dot is 1 cm from the next. Shape A is the one already done for you.

On this dot grid every dot is 1 cm from the next one. So each small step of a boundary is 1 cm. To find the perimeter, walk right round the shape and count the 1 cm steps. A B C D E The five shapes on the dot grid on page 92. Shape A is the one already done for you. Shape A (the one done for you): 2 + 1 + 1 + 1 + 3 + 2 = 10 cm , just as the book shows. Shape Where it is Adding the 1 cm steps Perimeter A top left, done for you 2 + 1 + 1 + 1 + 3 + 2 10 cm B long and thin, at the top 4 + 1 + 4 + 1 10 cm C the big one on the right 3 + 3 + 1 + 1 + 5 + 2 + 1 + 2 18 cm D the square at the bottom left 2 + 2 + 2 + 2 8 cm E the tall one in the middle 2 + 4 + 1 + 2 + 2 + 1 + 1 + 1 14 cm Why it happens: The dots are 1 cm apart, so the grid does the measuring for us. We only have to count the steps and add. Tip: Put a small mark at your starting corner. Stop counting when you get back to that mark.

Do any of the following shapes have the same perimeter? Tick them. A) B) C) D) E) F) The six shapes A) to F) on page 93, drawn on a 1 cm dot grid.

Yes. Count the 1 cm steps round each shape on the dot grid. A) B) C) D) E) F) The six shapes A) to F) on page 93, drawn on a 1 cm dot grid. Shape Adding the 1 cm steps Perimeter A) 4 + 1 + 1 + 1 + 3 + 2 12 cm B) 2 + 3 + 2 + 3 10 cm C) 2 + 1 + 1 + 2 + 1 + 1 + 2 + 2 12 cm D) 4 + 3 + 4 + 3 14 cm E) 1 + 2 + 3 + 1 + 4 + 3 14 cm F) 4 + 3 + 2 + 1 + 2 + 2 14 cm Tick these: A) and C) — both have a perimeter of 12 cm . D), E) and F) — all three have a perimeter of 14 cm . Only B) is left out. It is the only shape with a perimeter of 10 cm. Why it happens: D is a plain rectangle while E and F have steps in them. The steps push the boundary out and pull it back by the same amount, so the total stays 14 cm. Tip: For a rectangle you can add the long side and the short side, then double it. For D: 4 + 3 = 7, and 7 + 7 = 14 .

Estimate and measure the perimeters of shapes around you using a scale and write them in the space given below. S. No. Object Estimated perimeter in cm/m Actual measure in cm/m 1. Desk 2. Blackboard 3. Classroom floor 4. 5.

How to do it: First look at the thing and guess the total length all round it. Write that guess. Now measure each side with a scale or a measuring tape. Add all the sides. That sum is the perimeter. Use cm for small things and m for big things like the classroom floor. This is the table as it is printed in your book: S. No. Object Estimated perimeter in cm/m Actual measure in cm/m 1. Desk 2. Blackboard 3. Classroom floor 4. 5. 6. Sample answer (your classroom will give its own numbers): S. No. Object Estimated perimeter Actual measure How it was added 1. Desk 200 cm 200 cm 60 + 40 + 60 + 40 2. Blackboard 600 cm 590 cm 200 + 95 + 200 + 95 3. Classroom floor 30 m 28 m 8 + 6 + 8 + 6 4. My notebook 80 cm 86 cm 25 + 18 + 25 + 18 5. Classroom door 600 cm 580 cm 200 + 90 + 200 + 90 6. Window 400 cm 440 cm 120 + 100 + 120 + 100 Why it happens: The perimeter is the length of the boundary, so we simply add the lengths of all the sides that make that boundary. Tip: Measure the opposite sides of a rectangle too, to be sure they match. For a rectangle you can add one long side and one short side and then double the answer.

NCERT Solutions for Class 4th Maths Chapter 6 Fencing and Lacing (Perimeter) — Let Us Do

Book page 92 to 94 Updated on2026-09-19

Q1.

Bhola made the boundary of his gardens in the following ways. Circle the boundary that is longest.

Bhola’s three garden boundaries, drawn in bricks.

Answer

Bhola’s three garden boundaries, drawn in bricks.

Circle the third garden — the one with the steps sticking out on both sides.

How to check it yourself:

Take a piece of thread and lay it right along the boundary of the first garden.
Pinch the thread where it comes back to the start, and pull it straight against a scale.
Do the same for the other two gardens and compare the three lengths.

Garden 3 has the longest boundary
Garden 1 is a little shorter
Garden 2 has the shortest boundary

Why it happens: Garden 3 keeps going out and coming back in again. Every step that goes out must be walked back, so those extra bits make the boundary longer. Garden 2 has its corners cut off, and cutting a corner is a short cut — so its boundary is the shortest.

Tip: Gardens 1 and 3 hold about the same amount of soil, but their boundaries are not the same. Same space inside does not mean same boundary.

Q2.

Let us find the perimeter of some shapes using the dot grid. One is done for you.

The five shapes on the dot grid on page 92. Every dot is 1 cm from the next. Shape A is the one already done for you.

Answer

On this dot grid every dot is 1 cm from the next one. So each small step of a boundary is 1 cm. To find the perimeter, walk right round the shape and count the 1 cm steps.

The five shapes on the dot grid on page 92. Shape A is the one already done for you.

Shape A (the one done for you): 2 + 1 + 1 + 1 + 3 + 2 = 10 cm, just as the book shows.

Shape	Where it is	Adding the 1 cm steps	Perimeter
A	top left, done for you	2 + 1 + 1 + 1 + 3 + 2	10 cm
B	long and thin, at the top	4 + 1 + 4 + 1	10 cm
C	the big one on the right	3 + 3 + 1 + 1 + 5 + 2 + 1 + 2	18 cm
D	the square at the bottom left	2 + 2 + 2 + 2	8 cm
E	the tall one in the middle	2 + 4 + 1 + 2 + 2 + 1 + 1 + 1	14 cm

Why it happens: The dots are 1 cm apart, so the grid does the measuring for us. We only have to count the steps and add.

Tip: Put a small mark at your starting corner. Stop counting when you get back to that mark.

Q3.

a) Colour the boundary with the longest length in blue.

The five shapes on the dot grid on page 92. Every dot is 1 cm from the next. Shape A is the one already done for you.

Answer

Colour the boundary of shape C, the big one on the right, in blue. Its perimeter is 18 cm.

Shape C, the longest boundary, coloured blue.

A = 10 cm B = 10 cm C = 18 cm D = 8 cm E = 14 cm
18 is the biggest number

Why it happens: Shape C takes the most 1 cm steps to walk round, so its boundary is the longest.

Q4.

b) Colour the boundary with the shortest length in green.

The five shapes on the dot grid on page 92. Every dot is 1 cm from the next. Shape A is the one already done for you.

Answer

Colour the boundary of shape D, the square at the bottom left, in green. Its perimeter is 8 cm.

Shape D, the shortest boundary, coloured green.

A = 10 cm B = 10 cm C = 18 cm D = 8 cm E = 14 cm
8 is the smallest number
D is a square with each side 2 cm: 2 + 2 + 2 + 2 = 8

Why it happens: Shape D is the smallest of the five shapes, so walking round it takes the fewest 1 cm steps.

Q5.

c) Tick the shapes with the same length.

The five shapes on the dot grid on page 92. Every dot is 1 cm from the next. Shape A is the one already done for you.

Answer

Tick shape A and shape B. Both have a perimeter of 10 cm.

Shapes A and B, the two boundaries that are the same length.

A = 10 cm B = 10 cm
C = 18 cm D = 8 cm E = 14 cm
Only 10 comes twice

Why it happens: Shape B is long and thin and shape A is short and fat, yet both take 10 steps of 1 cm to go round. Shapes that look quite different can still have the same perimeter.

Q6.

Do any of the following shapes have the same perimeter? Tick them.

The six shapes A) to F) on page 93, drawn on a 1 cm dot grid.

Answer

Yes. Count the 1 cm steps round each shape on the dot grid.

The six shapes A) to F) on page 93, drawn on a 1 cm dot grid.

Shape	Adding the 1 cm steps	Perimeter
A)	4 + 1 + 1 + 1 + 3 + 2	12 cm
B)	2 + 3 + 2 + 3	10 cm
C)	2 + 1 + 1 + 2 + 1 + 1 + 2 + 2	12 cm
D)	4 + 3 + 4 + 3	14 cm
E)	1 + 2 + 3 + 1 + 4 + 3	14 cm
F)	4 + 3 + 2 + 1 + 2 + 2	14 cm

Tick these:

A) and C) — both have a perimeter of 12 cm.
D), E) and F) — all three have a perimeter of 14 cm.

Only B) is left out. It is the only shape with a perimeter of 10 cm.

Why it happens: D is a plain rectangle while E and F have steps in them. The steps push the boundary out and pull it back by the same amount, so the total stays 14 cm.

Tip: For a rectangle you can add the long side and the short side, then double it. For D: 4 + 3 = 7, and 7 + 7 = 14.

Q7.

Tick the garden with the minimum perimeter.

The three gardens on page 93, drawn on a 1 cm dot grid.

Answer

Tick the first garden, the plain rectangle. Its perimeter is the smallest, 18 cm.

The three gardens on page 93, drawn on a 1 cm dot grid.

Garden	Adding the 1 cm steps	Perimeter
1 (plain rectangle)	4 + 5 + 4 + 5	18 cm
2 (with a slot cut into the top)	2 + 2 + 1 + 2 + 2 + 5 + 5 + 5	24 cm
3 (narrow on top, wide below)	3 + 2 + 1 + 3 + 5 + 3 + 1 + 2	20 cm

18 cm, 20 cm, 24 cm
The smallest is 18 cm → garden 1

Why it happens: Minimum means the least. The slot in garden 2 adds two extra walls going in and one coming across, so its boundary grows a lot. The plain rectangle has no extra walls at all.

Did you know? A farmer who wants to spend the least on fencing picks the shape with the smallest perimeter.

Q8.

Estimate and measure the perimeters of shapes around you using a scale and write them in the space given below.

S. No.	Object	Estimated perimeter in cm/m	Actual measure in cm/m
1.	Desk
2.	Blackboard
3.	Classroom floor
4.
5.
6.

Answer

How to do it:

First look at the thing and guess the total length all round it. Write that guess.
Now measure each side with a scale or a measuring tape.
Add all the sides. That sum is the perimeter.
Use cm for small things and m for big things like the classroom floor.

This is the table as it is printed in your book:

S. No.	Object	Estimated perimeter in cm/m	Actual measure in cm/m
1.	Desk
2.	Blackboard
3.	Classroom floor
4.
5.
6.

Sample answer (your classroom will give its own numbers):

S. No.	Object	Estimated perimeter	Actual measure	How it was added
1.	Desk	200 cm	200 cm	60 + 40 + 60 + 40
2.	Blackboard	600 cm	590 cm	200 + 95 + 200 + 95
3.	Classroom floor	30 m	28 m	8 + 6 + 8 + 6
4.	My notebook	80 cm	86 cm	25 + 18 + 25 + 18
5.	Classroom door	600 cm	580 cm	200 + 90 + 200 + 90
6.	Window	400 cm	440 cm	120 + 100 + 120 + 100

Why it happens: The perimeter is the length of the boundary, so we simply add the lengths of all the sides that make that boundary.

Tip: Measure the opposite sides of a rectangle too, to be sure they match. For a rectangle you can add one long side and one short side and then double the answer.

Q9.

Draw three different shapes with perimeter of 20 cm.

Answer

On a 1 cm dot grid, draw shapes whose 1 cm steps add up to 20.

Three different shapes drawn on a 1 cm dot grid, each with a perimeter of 20 cm.

Shape	Adding the sides	Perimeter
A rectangle 6 cm by 4 cm	6 + 4 + 6 + 4	20 cm
A rectangle 7 cm by 3 cm	7 + 3 + 7 + 3	20 cm
An L shape	4 + 2 + 2 + 2 + 6 + 4	20 cm

You could also draw a square of side 5 cm, because 5 + 5 + 5 + 5 = 20.

Why it happens: For a rectangle, the long side and the short side together must make 10 cm, because 10 + 10 = 20. So 6 and 4, or 7 and 3, or 5 and 5 all work.

Try this: Cut a 20 cm piece of thread. Any closed shape you bend it into has a perimeter of 20 cm.

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