CBSE Class 5 Mental Maths Perimeter And Area Worksheet - Free Printable

Let's solve each question step by step and explain the reasoning.

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1. In which of the following situations, the concept of perimeter is involved:

(a) Carpeting of room?
(b) Fencing of plot?

- Answer: (b) Fencing of plot

Explanation:
Perimeter refers to the total length around the boundary of a shape.
- Carpeting a room involves covering the area inside the room → this is about area, not perimeter.
- Fencing a plot means enclosing the boundary → this involves the perimeter.

✔ So, perimeter is involved in (b).

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2. A triangle has sides 6 cm, 8 cm, and 10 cm. What is the perimeter of the triangle?

Solution:
Perimeter = sum of all sides
= 6 + 8 + 10 = 24 cm

✔ Answer: 24 cm

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3. Find the perimeter of a square whose one side is 4 cm long.

Solution:
All sides of a square are equal.
Perimeter = 4 × side = 4 × 4 = 16 cm

✔ Answer: 16 cm

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4. Find the perimeter of the rectangle whose sides are 5 cm and 2 cm.

Solution:
Perimeter of rectangle = 2 × (length + breadth)
= 2 × (5 + 2) = 2 × 7 = 14 cm

✔ Answer: 14 cm

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5. Find the perimeter of the given triangle:

Sides: 3 cm, 4 cm, 3.5 cm

Solution:
Perimeter = 3 + 4 + 3.5 = 10.5 cm

✔ Answer: 10.5 cm

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6. Find the perimeter of the rectangle given below:

Dimensions: 3.7 cm (length), 2.3 cm (breadth)

Solution:
Perimeter = 2 × (length + breadth)
= 2 × (3.7 + 2.3) = 2 × 6.0 = 12 cm

✔ Answer: 12 cm

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7. Which of the following figures has greater perimeter?

(a) Rectangle: 4 cm × 2 cm
(b) Square: 4 cm × 4 cm

Solution:

- Perimeter of (a): 2 × (4 + 2) = 2 × 6 = 12 cm
- Perimeter of (b): 4 × 4 = 16 cm

Since 16 > 12, (b) has greater perimeter.

✔ Answer: Figure (b)

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8. What is the perimeter of a triangle whose all sides are 4.5 cm long?

This is an equilateral triangle.

Solution:
Perimeter = 3 × side = 3 × 4.5 = 13.5 cm

✔ Answer: 13.5 cm

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9. Find the perimeter of the figure given below:

The figure is a polygon with the following side lengths:

From the diagram:
- Bottom base: 6.5 cm
- Two slanted sides on bottom: 2 cm each (left and right)
- Top horizontal parts: 3.5 cm and 3 cm (on left and right)
- Two upward slanted sides: 2.5 cm and 3 cm

Wait — let's list all outer edges carefully:

Looking at the shape:
- Left side: 2 cm (bottom) + 3.5 cm (horizontal) + 2.5 cm (upward slant)
- Right side: 2 cm (bottom) + 3 cm (horizontal) + 3 cm (upward slant)
- But we must add only the outer edges, not internal lines.

Actually, from the diagram:

We can trace the outer boundary:

Start from bottom-left corner:
1. 2 cm (left bottom)
2. 6.5 cm (base)
3. 2 cm (right bottom)
4. 3 cm (right top horizontal)
5. 3 cm (right upper slant)
6. 2.5 cm (left upper slant)
7. 3.5 cm (left top horizontal)

Wait — actually, looking at the figure:

It seems like a trapezoid-like shape with two "notches" or peaks on top.

But based on the labeling:

Let’s go clockwise:

- Start from bottom-left: 2 cm
- Then along bottom: 6.5 cm
- Then right-bottom: 2 cm
- Then up-right: 3 cm (horizontal top right)
- Then slant up: 3 cm
- Then slant down-left: 2.5 cm
- Then horizontal top-left: 3.5 cm
- Then back to start?

Wait — but that doesn't close.

Wait — better way: Let’s list all the outer sides as shown:

From the image:

- Left bottom: 2 cm
- Bottom: 6.5 cm
- Right bottom: 2 cm
- Right top horizontal: 3 cm
- Right slant: 3 cm
- Left slant: 2.5 cm
- Left top horizontal: 3.5 cm

Now check if it forms a closed shape.

But notice: The top part has two horizontal segments: 3.5 cm and 3 cm, and two slants: 2.5 cm and 3 cm.

So the entire boundary consists of:

1. 2 cm (left bottom)
2. 6.5 cm (bottom)
3. 2 cm (right bottom)
4. 3 cm (right top horizontal)
5. 3 cm (right slant)
6. 2.5 cm (left slant)
7. 3.5 cm (left top horizontal)

Wait — but the top is not connected directly. Let's visualize:

It looks like a symmetric shape with a peak in the middle.

But the labels show:

- Two 2 cm on the sides (bottom corners)
- Base: 6.5 cm
- Then going up: 3.5 cm and 3 cm horizontally on top
- Then two slants: 2.5 cm and 3 cm

But likely, the perimeter includes all outer edges.

So let’s list all the line segments forming the outer boundary:

From the diagram:

1. Left bottom: 2 cm
2. Bottom: 6.5 cm
3. Right bottom: 2 cm
4. Right top horizontal: 3 cm
5. Right slant: 3 cm
6. Left slant: 2.5 cm
7. Left top horizontal: 3.5 cm

Wait — but now we have a problem: the top has two horizontal parts: 3.5 cm and 3 cm, and two slants: 2.5 cm and 3 cm.

But how are they connected?

Looking at the diagram again:

- It starts from left bottom: 2 cm
- Then goes to 6.5 cm across
- Then up to 2 cm on right
- Then a horizontal segment of 3 cm (on top right)
- Then slant up 3 cm
- Then slant down 2.5 cm
- Then horizontal 3.5 cm on top left
- Then down to left bottom?

Wait — perhaps the shape is symmetric?

But more logically: the perimeter is the sum of all outer sides.

Let’s assume the figure is made of:

- Bottom: 6.5 cm
- Two vertical sides? No — no verticals.

Wait — the figure appears to be a zigzag shape.

Actually, looking at the labels:

From left to right:

- Left base: 2 cm
- Bottom: 6.5 cm
- Right base: 2 cm
- Then upward: 3.5 cm (left top horizontal), then 2.5 cm (slant), then 3 cm (slant), then 3 cm (right top horizontal)

Wait — no.

Better: the outer boundary consists of:

1. 2 cm (left bottom)
2. 6.5 cm (bottom)
3. 2 cm (right bottom)
4. 3 cm (right top horizontal)
5. 3 cm (right slant)
6. 2.5 cm (left slant)
7. 3.5 cm (left top horizontal)

But now, do these connect?

Yes — if you imagine:

- Start at bottom-left: go right 6.5 cm
- Then up 2 cm (but labeled 2 cm on right? No — the 2 cm is on both ends)

Wait — actually, the 2 cm on left and right are the vertical sides?

But the diagram shows:

- Bottom: 6.5 cm
- On left: 2 cm (probably vertical)
- On right: 2 cm (vertical)
- Then top has two horizontal parts: 3.5 cm and 3 cm
- And two slants: 2.5 cm and 3 cm

Ah! Likely:

- The figure has:
- Left side: 2 cm (vertical)
- Bottom: 6.5 cm
- Right side: 2 cm (vertical)
- Top: broken into two horizontal parts: 3.5 cm and 3 cm
- And two slants: 2.5 cm and 3 cm

But that doesn’t make sense unless the top is zigzag.

Actually, the correct interpretation:

The figure is a polygon with the following sides:

1. Left bottom: 2 cm (vertical)
2. Bottom: 6.5 cm (horizontal)
3. Right bottom: 2 cm (vertical)
4. Right top horizontal: 3 cm
5. Right slant: 3 cm (going up-left?)
6. Left slant: 2.5 cm (going down-right?)
7. Left top horizontal: 3.5 cm

Wait — this is confusing.

Let’s look at the standard interpretation of such problems.

In many textbooks, such a figure is a house-shaped or zigzag polygon.

But here’s the key: add all the labeled sides.

The figure has seven sides:

- 2 cm (left vertical)
- 6.5 cm (bottom)
- 2 cm (right vertical)
- 3 cm (right top horizontal)
- 3 cm (right slant)
- 2.5 cm (left slant)
- 3.5 cm (left top horizontal)

Wait — but the top has two horizontal segments: 3.5 cm and 3 cm, and two slants: 2.5 cm and 3 cm.

But the total top is not continuous.

Actually, the figure is likely:

- Starts at bottom-left: 2 cm up
- Then 3.5 cm right
- Then 2.5 cm up and right (slant)
- Then 3 cm down and right (slant)
- Then 3 cm right
- Then 2 cm down
- Then 6.5 cm left

No — that doesn’t work.

Wait — best way: just add all the outer edges as labeled.

From the diagram:

The outer boundary consists of:

1. Left vertical: 2 cm
2. Bottom: 6.5 cm
3. Right vertical: 2 cm
4. Right top horizontal: 3 cm
5. Right slant: 3 cm
6. Left slant: 2.5 cm
7. Left top horizontal: 3.5 cm

Wait — but now the top has two horizontal parts: 3.5 cm and 3 cm, and two slants: 2.5 cm and 3 cm.

But how are they arranged?

Possibly:

- From bottom-left: go up 2 cm
- Then go right 3.5 cm
- Then go up-slant 2.5 cm
- Then go down-slant 3 cm
- Then go right 3 cm
- Then go down 2 cm
- Then go left 6.5 cm

That would close.

But then the bottom is 6.5 cm, so yes.

So the perimeter is the sum of all these outer edges:

List:

- 2 cm (left vertical)
- 3.5 cm (top left horizontal)
- 2.5 cm (left slant)
- 3 cm (right slant)
- 3 cm (top right horizontal)
- 2 cm (right vertical)
- 6.5 cm (bottom)

Wait — but bottom is already included.

But in this path:

1. Left vertical: 2 cm
2. Top left horizontal: 3.5 cm
3. Left slant: 2.5 cm
4. Right slant: 3 cm
5. Top right horizontal: 3 cm
6. Right vertical: 2 cm
7. Bottom: 6.5 cm

Yes — that’s all seven sides.

So perimeter = sum of all sides:

= 2 + 3.5 + 2.5 + 3 + 3 + 2 + 6.5

Now calculate:

- 2 + 3.5 = 5.5
- +2.5 = 8
- +3 = 11
- +3 = 14
- +2 = 16
- +6.5 = 22.5 cm

✔ Answer: 22.5 cm

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✔ Final Answers:

1. (b) Fencing of plot
2. 24 cm
3. 16 cm
4. 14 cm
5. 10.5 cm
6. 12 cm
7. Figure (b)
8. 13.5 cm
9. 22.5 cm

Let me know if you'd like a visual explanation for #9!