RBSE Solutions Class 5 Maths Chapter 14 Perimeter and Area Exercise 14.1

Rajasthan Board RBSE Class 5 Maths Chapter 14 Perimeter and Area Ex 14.1

 

Question 1. Find out the perimeter of given shapes.
Answer:

(a) For the first shape, we add up the lengths of all its sides: \( 10 + 7 + 10 + 8 + 7 + 7 + 9 + 7 = 65 \) cm.
(b) For the second shape, we sum the lengths of all its sides: \( 10 + 5 + 4 + 5 + 5 + 4 + 5 = 38 \) cm.
(c) The third shape is a square with each side measuring 7 cm. The perimeter of a square is calculated by multiplying the length of one side by 4: \( 4 \times 7 = 28 \) cm. A square has four equal sides, making this calculation straightforward.
In simple words: To find the perimeter, just add up the lengths of all the outside edges of the shape. For a square, you can simply multiply one side's length by four.

🎯 Exam Tip: Always ensure you add *all* the side lengths when calculating the perimeter of irregular shapes, not just the visible ones. For regular polygons, remember the formula (e.g., \( \text{Perimeter} = \text{number of sides} \times \text{side length} \)).

 

Question 2. Find out the perimeter of rectangular shapes with given measurements :
(a) Length = 30 cm., Width = 48 cm.
(b) Length = 20 cm., Width = 34 cm.
(c) Length = 60 cm., Width = 20 cm.
(d) Length = 30 cm., Width = 12 cm.
Answer:
(a) Length \( = 30 \) cm, Width \( = 48 \) cm.
Perimeter \( = 2 \times (\text{Length} + \text{Width}) \)
\( = 2 \times (30 + 48) \)
\( = 2 \times 78 \)
\( = 156 \) cm. This formula accounts for both pairs of equal sides in a rectangle.

(b) Length \( = 20 \) cm, Width \( = 34 \) cm.
Perimeter \( = 2 \times (\text{Length} + \text{Width}) \)
\( = 2 \times (20 + 34) \)
\( = 2 \times 54 \)
\( = 108 \) cm.

(c) Length \( = 60 \) cm, Width \( = 20 \) cm.
Perimeter \( = 2 \times (\text{Length} + \text{Width}) \)
\( = 2 \times (60 + 20) \)
\( = 2 \times 80 \)
\( = 160 \) cm.

(d) Length \( = 30 \) cm, Width \( = 12 \) cm.
Perimeter \( = 2 \times (\text{Length} + \text{Width}) \)
\( = 2 \times (30 + 12) \)
\( = 2 \times 42 \)
\( = 84 \) cm.
In simple words: To find the perimeter of a rectangle, add its length and width together, then multiply the sum by 2. This is because a rectangle has two equal lengths and two equal widths.

🎯 Exam Tip: Always remember the formula for the perimeter of a rectangle is \( 2 \times (\text{Length} + \text{Width}) \). Double-check your addition before multiplying to avoid errors.

 

Question 3. Find out the perimeter of following regular shapes with the help of formula.
Answer:

(a) The first shape is a triangle with all sides equal to 14 cm. Since it's a regular triangle (equilateral), its perimeter is found by multiplying the side length by 3: \( 3 \times 14 = 42 \) cm.
(b) The second shape is a square with each side measuring 6 cm. For a square, the perimeter is calculated by multiplying the side length by 4: \( 4 \times 6 = 24 \) cm.
In simple words: For shapes where all sides are the same length, just count the number of sides and multiply that by the length of one side. This gives you the total distance around the shape.

🎯 Exam Tip: Always identify if a shape is regular (all sides and angles equal) or irregular. For regular polygons, use the shortcut formula (number of sides × side length). For irregular shapes, sum all individual side lengths.

 

Question 4. Vijay has made a rectangle. Find its perimeter and area?
Answer:

The rectangle made by Vijay has a length of 5 cm and a width of 3 cm.
Perimeter of the rectangle \( = 2 \times (\text{Length} + \text{Width}) \)
\( = 2 \times (5 + 3) \)
\( = 2 \times 8 \)
\( = 16 \) cm.
Area of the rectangle \( = \text{Length} \times \text{Width} \)
\( = 5 \times 3 \)
\( = 15 \) square cm. For a rectangle, the area is simply the product of its length and width.
In simple words: Vijay's rectangle is 5 cm long and 3 cm wide. Its perimeter (distance around) is 16 cm, and its area (space inside) is 15 square cm.

🎯 Exam Tip: Remember that perimeter is a linear measurement (in cm, m) and area is a square measurement (in sq. cm, sq. m). Always include the correct units in your final answer.

 

Question 5. Length and width of a rectangular field are 25 meter and 30 meter respectively. Find its area?
Answer:
Length of the rectangular field \( = 25 \) meter.
Width of the rectangular field \( = 30 \) meter.
Area of the rectangular field \( = \text{Length} \times \text{Width} \)
\( = 25 \times 30 \)
\( = 750 \) square meter. The area tells us how much space the field covers on the ground.
In simple words: To find the area of the rectangular field, multiply its length (25 meters) by its width (30 meters). The answer is 750 square meters.

🎯 Exam Tip: Always state the units clearly. Area is always measured in square units (e.g., square meters, square cm).

 

Question 6. Length and width of a rectangular towel are 125 cm and 60 cm respectively. What will be the perimeter of the towel?
Answer:
Length of the rectangular towel \( = 125 \) cm.
Width of the rectangular towel \( = 60 \) cm.
Perimeter of the rectangular towel \( = 2 \times (\text{Length} + \text{Width}) \)
\( = 2 \times (125 + 60) \)
\( = 2 \times 185 \)
\( = 370 \) cm. Calculating the perimeter helps in knowing the amount of lace needed to border the towel.
In simple words: To find the perimeter of the towel, add its length (125 cm) and width (60 cm) together. Then, multiply that sum by 2. The perimeter is 370 cm.

🎯 Exam Tip: Pay attention to the units given in the question (cm, m). Ensure your final answer uses the correct unit for perimeter, which is a linear measure.

 

Question 7. A square field needs 260 meter long barbed wire for throughout fencing. Find its one side?
Answer:
The total length of barbed wire needed for fencing represents the perimeter of the square field.
Perimeter of square \( = 260 \) meter.
Formula for perimeter of a square \( = 4 \times \text{side} \)
So, \( 4 \times \text{side} = 260 \) meter
\( \text{Side of square} = \frac{260}{4} \)
\( = 65 \) meter. This means each boundary of the field is 65 meters long.
In simple words: The fence wire (260 meters) is the perimeter of the square field. Since a square has 4 equal sides, divide the total wire length by 4 to find the length of one side. Each side is 65 meters.

🎯 Exam Tip: When given the perimeter of a square and asked for its side, always divide the perimeter by 4, as all four sides are equal.

 

Question 8. A room floor is 8 meter and 7 meter respectively. Find the area of the room floor.
Answer:
Length of the room floor \( = 8 \) meter.
Width of the room floor \( = 7 \) meter.
Area of the room floor \( = \text{Length} \times \text{Width} \)
\( = 8 \times 7 \)
\( = 56 \) square meter. This calculation is essential for knowing how much flooring material is needed.
In simple words: To find the area of the room floor, multiply its length (8 meters) by its width (7 meters). The area is 56 square meters.

🎯 Exam Tip: Always confirm if the question asks for perimeter or area. For area, the units will always be square units.

 

Question 9. Find out the perimeter of a square stool, whose side is 60 centimeter.
Answer:
Side of the square stool \( = 60 \) centimeter.
Perimeter of a square stool \( = 4 \times \text{side} \)
\( = 4 \times 60 \)
\( = 240 \) centimeter. This is the total length around the edges of the stool.
In simple words: The stool is a square, and one side is 60 cm. To get the perimeter, multiply 60 cm by 4. The perimeter is 240 cm.

🎯 Exam Tip: Always remember that a square has four equal sides. So, its perimeter is simply four times the length of one side.

 

Question 10. To take around of a square field, Dev had to walk 40 meters. Find the side of the square field.
Answer:
Distance walked in two rounds around the square field \( = 40 \) meters.
To find the distance in one round, we divide the total distance by 2:
Distance walked in one round \( = \frac{40}{2} = 20 \) meters.
This distance for one round is the perimeter of the square field.
So, Perimeter of the square field \( = 20 \) meters.
Since the perimeter of a square \( = 4 \times \text{side} \), we have:
\( 4 \times \text{side} = 20 \) meters
\( \text{Side of square field} = \frac{20}{4} \)
\( = 5 \) meters. Each side of the square field is 5 meters long, which is a common size for smaller fields.
In simple words: Dev walked 40 meters in two rounds around a square field. So, one round is 20 meters (40 divided by 2). This 20 meters is the perimeter. To find one side of the square, divide the perimeter by 4. Each side is 5 meters.

🎯 Exam Tip: Read the question carefully to identify if the given distance covers one round or multiple rounds. Adjust the perimeter value accordingly before calculating the side length.