Math worksheet with perimeter calculation problems for different geometric shapes.

Let's solve each problem step by step.

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

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

Solution:
- Carpeting of room: This involves covering the floor area of the room, so it deals with the area, not the perimeter.
- Fencing of plot: This involves enclosing the boundary of the plot, so it deals with the perimeter.

Answer: (b) Fencing of plot

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

Solution:
The perimeter of a triangle is the sum of the lengths of its three sides.
\[
\text{Perimeter} = 6 \, \text{cm} + 8 \, \text{cm} + 10 \, \text{cm} = 24 \, \text{cm}
\]

Answer: 24 cm

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

Solution:
The perimeter of a square is given by:
\[
\text{Perimeter} = 4 \times \text{side length}
\]
Here, the side length is 4 cm.
\[
\text{Perimeter} = 4 \times 4 \, \text{cm} = 16 \, \text{cm}
\]

Answer: 16 cm

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

Solution:
The perimeter of a rectangle is given by:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width})
\]
Here, the length is 5 cm and the width is 2 cm.
\[
\text{Perimeter} = 2 \times (5 \, \text{cm} + 2 \, \text{cm}) = 2 \times 7 \, \text{cm} = 14 \, \text{cm}
\]

Answer: 14 cm

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Question 5: Find the perimeter of the given triangle:

The triangle has sides 3 cm, 4 cm, and 3.5 cm.

Solution:
The perimeter of a triangle is the sum of the lengths of its three sides.
\[
\text{Perimeter} = 3 \, \text{cm} + 4 \, \text{cm} + 3.5 \, \text{cm} = 10.5 \, \text{cm}
\]

Answer: 10.5 cm

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Question 6: Find the perimeter of the rectangle given below:

The rectangle has sides 3.7 cm and 2.3 cm.

Solution:
The perimeter of a rectangle is given by:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width})
\]
Here, the length is 3.7 cm and the width is 2.3 cm.
\[
\text{Perimeter} = 2 \times (3.7 \, \text{cm} + 2.3 \, \text{cm}) = 2 \times 6 \, \text{cm} = 12 \, \text{cm}
\]

Answer: 12 cm

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Question 7: Which of the following figures has greater perimeter?

#### Figure (a): Rectangle with sides 4 cm and 2 cm
The perimeter of the rectangle is:
\[
\text{Perimeter} = 2 \times (4 \, \text{cm} + 2 \, \text{cm}) = 2 \times 6 \, \text{cm} = 12 \, \text{cm}
\]

#### Figure (b): Square with side 4 cm
The perimeter of the square is:
\[
\text{Perimeter} = 4 \times 4 \, \text{cm} = 16 \, \text{cm}
\]

Comparison:
- Perimeter of figure (a): 12 cm
- Perimeter of figure (b): 16 cm

Answer: Figure (b) has the greater perimeter.

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

Solution:
Since all sides of the triangle are equal (it is an equilateral triangle), the perimeter is:
\[
\text{Perimeter} = 3 \times \text{side length}
\]
Here, the side length is 4.5 cm.
\[
\text{Perimeter} = 3 \times 4.5 \, \text{cm} = 13.5 \, \text{cm}
\]

Answer: 13.5 cm

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Question 9: Find the perimeter of the figure given below:

The figure is a combination of a triangle and a trapezoid. The sides are:
- Top side: 6.5 cm
- Left side: 2 cm
- Bottom left side: 3.5 cm
- Bottom right side: 3 cm
- Right side: 2 cm
- Top triangle side: 2.5 cm

Solution:
The perimeter is the sum of all the outer sides of the figure.
\[
\text{Perimeter} = 6.5 \, \text{cm} + 2 \, \text{cm} + 3.5 \, \text{cm} + 3 \, \text{cm} + 2 \, \text{cm} + 2.5 \, \text{cm}
\]
\[
\text{Perimeter} = 19.5 \, \text{cm}
\]

Answer: 19.5 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. 19.5 cm

\boxed{1. \text{(b)}, 2. 24 \, \text{cm}, 3. 16 \, \text{cm}, 4. 14 \, \text{cm}, 5. 10.5 \, \text{cm}, 6. 12 \, \text{cm}, 7. \text{(b)}, 8. 13.5 \, \text{cm}, 9. 19.5 \, \text{cm}}