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Fields and Fences - Perimeter of Rectangles and Squares

Grade 4CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The perimeter is the total distance around the boundary of a closed shape. For a rectangle, the boundary consists of two lengths and two breadths.

A rectangle showing length and breadth labels on all four sides.
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The formula for the perimeter of a rectangle is P=2×(Length+Breadth)P = 2 \times (Length + Breadth). This is because opposite sides of a rectangle are equal.

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A square is a special rectangle where all four sides are equal. Therefore, the perimeter of a square is calculated as P=4×SideP = 4 \times Side.

A square showing all four sides labeled as s.
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For irregular shapes or polygons, the perimeter is simply the sum of the lengths of all its outer sides.

📐Formulae

Perimeter of a Rectangle=2×(Length+Breadth)\text{Perimeter of a Rectangle} = 2 \times (Length + Breadth)

Perimeter of a Square=4×Side\text{Perimeter of a Square} = 4 \times Side

Side of a Square=Perimeter4\text{Side of a Square} = \frac{\text{Perimeter}}{4}

Perimeter of any shape=Sum of all sides\text{Perimeter of any shape} = \text{Sum of all sides}

💡Examples

Problem 1:

A rectangular garden has a length of 15 m15\text{ m} and a breadth of 10 m10\text{ m}. Find the length of the fence required to cover the boundary of the garden.

Solution:

Given: Length (ll) = 15 m15\text{ m}, Breadth (bb) = 10 m10\text{ m}. Using the formula: Perimeter=2×(l+b)\text{Perimeter} = 2 \times (l + b) Perimeter=2×(15+10)\text{Perimeter} = 2 \times (15 + 10) Perimeter=2×25\text{Perimeter} = 2 \times 25 Perimeter=50 m\text{Perimeter} = 50\text{ m}. The length of the fence required is 50 m50\text{ m}.

Explanation:

To find the total boundary of a rectangle, we add the length and breadth and then multiply by 2 because there are two lengths and two breadths in a rectangle.

Problem 2:

Rohan runs around a square park whose side is 25 m25\text{ m}. How much distance does he cover in one complete round?

Solution:

Given: Side of the square park = 25 m25\text{ m}. Using the formula: Perimeter=4×Side\text{Perimeter} = 4 \times Side Perimeter=4×25\text{Perimeter} = 4 \times 25 Perimeter=100 m\text{Perimeter} = 100\text{ m}. Rohan covers 100 m100\text{ m} in one round.

Explanation:

Since a square has four equal sides, multiplying the length of one side by 4 gives the total distance around the park.

Problem 3:

A farmer has a rectangular field of length 40 m40\text{ m} and breadth 25 m25\text{ m}. He wants to put a wire fence around it three times. What is the total length of the wire he needs?

Rectangle representing a field with length 40m and breadth 25m.

Solution:

Length (l)=40 m\text{Length (l)} = 40\text{ m} Breadth (b)=25 m\text{Breadth (b)} = 25\text{ m} Perimeter=2×(40+25)\text{Perimeter} = 2 \times (40 + 25) Perimeter=2×65=130 m\text{Perimeter} = 2 \times 65 = 130\text{ m} Wire for 3 rounds=3×130=390 m\text{Wire for 3 rounds} = 3 \times 130 = 390\text{ m}

Explanation:

First, calculate the perimeter of the field for one round of fencing. Since the farmer needs to fence it three times, multiply the perimeter by 33.

Problem 4:

A square photo frame has a perimeter of 80 cm80\text{ cm}. Find the length of each side of the frame.

A square frame with perimeter 80 cm and an unknown side length.

Solution:

Perimeter=80 cm\text{Perimeter} = 80\text{ cm} Side=Perimeter4\text{Side} = \frac{\text{Perimeter}}{4} Side=804=20 cm\text{Side} = \frac{80}{4} = 20\text{ cm}

Explanation:

In a square, all four sides are equal. If we know the total boundary length (perimeter), we divide it by 44 to find the length of one side.

Perimeter of Rectangles and Squares Class 4 Notes & Examples