RBSE Solutions Class 6 Maths Chapter 14 Perimeter and Area Exercise 14.1

Question 1. Find the perimeter of each of the following figures:
Answer: The perimeter of a figure is the total length of its boundary. We add up the lengths of all the sides to find it.
(i) For the first figure, the perimeter is calculated by adding all its side lengths:
\( 2 + 5 + 1 + 3.5 + 3.5 + 1 + 5 = 21 \) cm.
(ii) For the second figure, the perimeter is the sum of all its sides:
\( 1 + 8 + 4 + 5 + 1 + 4 + 3 + 8 + 1 + 8 + 4 + 5 + 1 + 4 + 3 + 8 = 68 \) cm.
(iii) For the third figure, the perimeter is found by adding up all its sides:
\( 6 + 6 + 2 + 2 + 2 + 2 + 2 + 2 = 24 \) cm. This figure has eight sides.
In simple words: The perimeter is how long the outside edge of a shape is. We add up all the side lengths of each figure to get its perimeter.

🎯 Exam Tip: Always make sure to count every side and add its length carefully when calculating perimeter, especially for irregular shapes, to avoid missing any part of the boundary.

Question 2. Find the perimeter of a regular pentagon with each side equal to 4 cm.
Answer: A regular pentagon has five sides, and all its sides are equal in length. To find the perimeter, we multiply the length of one side by the number of sides. Each side is 4 cm long.
Perimeter = Number of sides \( \times \) Length of one side
Perimeter \( = 5 \times 4 \) cm
Perimeter \( = 20 \) cm. So, the total length around the pentagon is 20 cm.
In simple words: A pentagon has 5 equal sides. So, for a 4 cm side, the perimeter is 5 times 4, which is 20 cm.

🎯 Exam Tip: Remember that "regular" means all sides are the same length, which simplifies perimeter calculation to side length multiplied by the number of sides.

Question 3. A piece of string is 36 cm long. What will be the length of each side if the string is used to form:
(i) a square?
(ii) an equilateral?
(iii) a regular hexagon?
Answer: The total length of the string is 36 cm, which will be the perimeter of the shape formed. To find the length of each side, we divide the total length of the string by the number of sides in the shape.
(i) If the string forms a square, it has 4 equal sides.
Length of each side \( = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{36}{4} = 9 \) cm.
Each side of the square will be 9 cm long. A square has four equal sides.
(ii) If the string forms an equilateral triangle, it has 3 equal sides.
Length of each side \( = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{36}{3} = 12 \) cm.
Each side of the equilateral triangle will be 12 cm long. All three sides of an equilateral triangle are of the same length.
(iii) If the string forms a regular hexagon, it has 6 equal sides.
Length of each side \( = \frac{\text{Perimeter}}{\text{Number of sides}} = \frac{36}{6} = 6 \) cm.
Each side of the regular hexagon will be 6 cm long. A regular hexagon is a six-sided shape with all sides equal.
In simple words: We have a 36 cm string. To find each side's length, we divide 36 by the number of sides of the shape (4 for a square, 3 for an equilateral triangle, 6 for a regular hexagon).

🎯 Exam Tip: Understand the properties of regular polygons; knowing the number of equal sides is key to quickly solving perimeter problems for such shapes.

Question 4. Geeta runs around a square field of side 50 m. Pooja runs around a rectangular field with length 65 m and breadth 25 m. Who covers less distance?
Answer: We need to calculate the perimeter for both Geeta and Pooja to see who covers less distance. The person who runs around the field with the smaller perimeter will cover less distance.
First, let's find the distance Geeta covers:
Geeta runs around a square field with a side of 50 m.
Perimeter of square \( = 4 \times \text{side} \)
Perimeter of Geeta's field \( = 4 \times 50 \) m \( = 200 \) m.
Next, let's find the distance Pooja covers:
Pooja runs around a rectangular field with length 65 m and breadth 25 m.
Perimeter of rectangle \( = 2 \times (\text{length} + \text{breadth}) \)
Perimeter of Pooja's field \( = 2 \times (65 + 25) \) m \( = 2 \times 90 \) m \( = 180 \) m.
Now, compare the distances:
Geeta covers 200 m, and Pooja covers 180 m.
Since \( 180 < 200 \), Pooja covers less distance (by \( 200 - 180 = 20 \) m). A smaller perimeter means a shorter path around the shape.
In simple words: Geeta runs 200 m around a square. Pooja runs 180 m around a rectangle. Pooja runs less distance.

🎯 Exam Tip: Always calculate the full perimeter for each shape and then compare the total distances to determine who covers more or less.

Question 5. Find the side of the regular pentagon whose perimeter is 30 cm.
Answer: A regular pentagon has five equal sides. If we know the total perimeter, we can find the length of one side by dividing the perimeter by the number of sides.
Perimeter of regular pentagon \( = 30 \) cm.
Number of sides in a pentagon \( = 5 \).
Length of each side \( = \frac{\text{Perimeter}}{\text{Number of sides}} \)
Length of each side \( = \frac{30}{5} \) cm \( = 6 \) cm.
So, each side of the regular pentagon is 6 cm long. This method works for any regular polygon.
In simple words: A regular pentagon has 5 equal sides. Since the total distance around is 30 cm, each side is 30 divided by 5, which is 6 cm.

🎯 Exam Tip: For regular polygons, the formula "Perimeter = Number of Sides × Length of One Side" can be rearranged to find any missing value if the others are known.

Question 6. Madhu has a rectangular field of length 23.5 m and breadth 15.5 m respectively. He wants to fence his field with steel wire. What is the total length of steel wire he must use?
Answer: To fence a field, Madhu needs to cover the entire boundary of the field. This means he needs to find the perimeter of the rectangular field. The perimeter of a rectangle is found by adding up all its four sides.
Length of the rectangular field \( (l) = 23.5 \) m.
Breadth of the rectangular field \( (b) = 15.5 \) m.
Perimeter of the field \( = 2 \times (l + b) \)
Perimeter \( = 2 \times (23.5 + 15.5) \) m
Perimeter \( = 2 \times (39) \) m
Perimeter \( = 78 \) m.
Therefore, Madhu must use 78 m of steel wire for fencing. Fencing ensures the field is enclosed from all sides.
In simple words: Madhu needs to find the perimeter of his rectangular field to fence it. Adding the length and breadth and then multiplying by two gives 78 m of wire.

🎯 Exam Tip: Remember that "fencing" always implies calculating the perimeter of a shape, as it involves enclosing the area along its boundary.

Question 7. Perimeter of a football ground is 270 m. Find the breadth of the ground if the length of the ground is 90 m.
Answer: A football ground is usually rectangular. We are given the perimeter and the length, and we need to find the breadth. The formula for the perimeter of a rectangle is \( P = 2 \times (l + b) \).
Perimeter of ground \( (P) = 270 \) m.
Length of ground \( (l) = 90 \) m.
Using the perimeter formula:
\( 2 \times (l + b) = P \)
\( 2 \times (90 + b) = 270 \)
First, divide the perimeter by 2 to get the sum of length and breadth:
\( 90 + b = \frac{270}{2} \)
\( 90 + b = 135 \)
Now, subtract the length from this sum to find the breadth:
\( b = 135 - 90 \)
\( b = 45 \) m.
So, the breadth of the football ground is 45 m. We can always find a missing side if the perimeter and other sides are known.
In simple words: The perimeter of a rectangle is 2 times (length + breadth). If the perimeter is 270 m and length is 90 m, then 90 plus breadth must be half of 270 (which is 135). So, the breadth is 135 minus 90, making it 45 m.

🎯 Exam Tip: When given the perimeter and one side of a rectangle, first divide the perimeter by two to find the sum of length and breadth, then subtract the known side to find the unknown side.