NCERT Solutions for Class 5th Maths Chapter 11 Two gardens on a grid, your palm, leaves, and the two mats — Let Us Do
Book page 145–147 Updated on2026-09-19
Q1.
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.
The two gardens on a square grid, with a path between them. Each small square is 1 cm by 1 cm.
Answer
Area of Garden A = 10 square cm. Area of Garden B = 12 square cm. Garden B is bigger, by 2 square cm.
Garden A is 2 wide and 5 tall. Garden B is 4 wide and 3 tall. The cream strip between them is the path.
Look at Garden A. It is 2 squares wide and 5 squares tall.
Count or multiply. 2 × 5 = 10 squares. Each square is 1 square cm, so the area is 10 square cm.
Look at Garden B. It is 4 squares wide and 3 squares tall.
Count or multiply. 4 × 3 = 12 squares, that is 12 square cm.
Compare. 12 − 10 = 2, so Garden B has 2 square cm more.
Area of Garden A = 2 × 5 = 10 square cm Area of Garden B = 4 × 3 = 12 square cm Difference = 12 − 10 = 2 square cm
Observations to share: Garden A looks taller, and a tall shape can trick the eye into looking bigger. But Garden B, although shorter, is twice as wide. On the grid the eye cannot cheat — we simply count squares, and B covers two more of them.
Tip: The book writes the unit as “cm square”. We usually say square cm. Both mean the same thing: how many 1 cm × 1 cm squares fit inside.
Q2.
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?
The square grid for tracing your palm. Each small square is 1 cm by 1 cm.
Answer
Method: trace, then count whole squares first and half squares afterwards. A Class 5 palm usually comes to about 50 to 70 square cm.
Trace. Put your open palm flat on the grid, fingers together, and draw round it with a pencil.
Count the full squares. Mark a dot in every square that is completely inside the outline. Suppose you get 46.
Count the part squares. Now look at the squares that the outline cuts. Count a square if more than half of it is inside; leave it out if less than half is inside. Suppose you get 12 more.
Add. 46 + 12 = 58 squares, so the area is about 58 square cm.
Compare with a friend. The bigger number means the bigger palm.
Full squares = 46 Part squares counted in = 12 Approximate area of palm = 46 + 12 = about 58 square cm
Why we say “approximate”: A palm has curved edges, so it never lands neatly on the grid lines. Counting the more-than-half squares and dropping the less-than-half ones balances out — some are a little too much, some a little too little, and the errors cancel.
Sample answer: “My palm covered about 58 square cm. Meera's palm covered about 54 square cm. So my palm is bigger, by about 4 square cm.”
Q3.
Collect leaves of different kinds. Put them on a square grid and find their area. (a) Name the leaf with the largest area.
Answer
The biggest leaf is usually the banyan or the peepal leaf. Measure them the same way you measured your palm.
Collect fallen leaves — neem, peepal, banyan, mango, tulsi. Do not pluck them from the tree.
Place one leaf flat on the grid and draw round it.
Count full squares, then the more-than-half squares, and add.
Write each leaf's area in a table and pick the largest number.
Leaf
Full squares
Part squares counted
Area
Banyan
34
10
about 44 square cm
Peepal
26
9
about 35 square cm
Mango
14
6
about 20 square cm
Neem
3
2
about 5 square cm
Tulsi
1
2
about 3 square cm
Largest area = 44 square cm → the banyan leaf
Sample answer: “The leaf with the largest area is the banyan leaf. It covered about 44 square cm on the grid.” Your own answer will depend on the leaves you collect — write down what you actually measured.
Q4.
Collect leaves of different kinds. Put them on a square grid and find their area. (b) Name the leaf with the smallest area.
Answer
The smallest leaf is usually the tulsi leaf — in the table above it covered only about 3 square cm.
Look at the same table you made in part (a).
Find the smallest number in the area column. Here it is 3 square cm.
Name that leaf. Tulsi.
Smallest area = 3 square cm → the tulsi leaf Banyan (44) is about 14 times bigger than tulsi (3)
Why the grid is the fair way to decide: A leaf can be long and thin, like a neem leaflet, or short and wide, like a peepal leaf. Looking at length alone would give the wrong answer. Counting squares measures the whole surface, so the comparison is fair.
Sample answer: “The leaf with the smallest area is the tulsi leaf. It covered about 3 square cm.”
Q5.
The following mats are made of square patches of equal size. How many square patches will be required to cover each mat? Trace and cut out a small square of the size given below and find the area. Mat (a): Area = ______ Perimeter = ______
Answer
Mat (a) needs 10 square patches. Area = 10 square units. Perimeter = 14 units.
Ten patches fill the mat exactly. Its border is 5 + 2 + 5 + 2 = 14 units long.
Lay the little square along the top of the mat. It fits 5 times.
Lay it down the side. It fits 2 times.
Multiply for the area. 5 × 2 = 10 patches, so the area is 10 square units.
Add the four sides for the perimeter. 5 + 2 + 5 + 2 = 14 units.
Area of mat (a) = 5 × 2 = 10 square units Perimeter of mat (a) = 5 + 2 + 5 + 2 = 14 units
Why area and perimeter are counted so differently: For the area you count the patches inside — the cloth. For the perimeter you measure the edge outside — the ribbon. One is about filling, the other is about going round.
Q6.
The following mats are made of square patches of equal size. How many square patches will be required to cover each mat? Mat (b): Area = ______ Perimeter = ______
Answer
Mat (b) needs 12 square patches. Area = 12 square units. Perimeter = 14 units.
Twelve patches fill this mat. Its border is 4 + 3 + 4 + 3 = 14 units long — the same as mat (a).
Lay the little square along the top. It fits 4 times.
Lay it down the side. It fits 3 times.
Multiply for the area. 4 × 3 = 12 patches, so the area is 12 square units.
Add the four sides for the perimeter. 4 + 3 + 4 + 3 = 14 units.
Area of mat (b) = 4 × 3 = 12 square units Perimeter of mat (b) = 4 + 3 + 4 + 3 = 14 units
Something surprising: Mat (a) and mat (b) have the same perimeter, 14 units, but different areas — 10 and 12. The same length of ribbon can go round two mats that need different amounts of cloth. The squarer a shape is, the more it holds.
Q7.
Would both mats require an equal or different number of patches?
Answer
A different number. Mat (a) needs 10 patches and mat (b) needs 12 patches, so mat (b) needs 2 patches more.
Same border of 14 units, but mat (b) holds two more patches.
Why the squarer mat holds more: Both mats use 14 units of edge. Mat (a) spends most of that edge on being long and thin, so it stays skinny. Mat (b) spreads its edge more evenly, 4 and 3 instead of 5 and 2, so it becomes fatter and holds more patches. Out of all the shapes with the same perimeter, the one closest to a square holds the most.
Try This: Take 14 units of edge and try 6 + 1: that mat holds only 6 patches. Now try 4 + 3: it holds 12. The closer the two numbers, the more it holds.