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Perimeter, Area and Volume - Perimeter of Square and Rectangle

Grade 5ICSE

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

🔑Concepts

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The perimeter is the total length of the boundary of a closed figure. For a rectangle, it is the sum of all four sides, where opposite sides are equal.

Rectangle diagram showing length and breadth labels on opposite sides.
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A square is a special rectangle where all four sides are equal in length. Therefore, the perimeter is simply four times the length of one side.

Square diagram showing all four sides labeled as 's'.
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To find the length of a side of a square when the perimeter is given, we divide the total perimeter by 4.

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If the perimeter and one dimension (length or breadth) of a rectangle are known, the other dimension can be found by subtracting the known dimension from half of the perimeter.

📐Formulae

Perimeter of a Rectangle=2×(l+b)Perimeter\ of\ a\ Rectangle = 2 \times (l + b)

Perimeter of a Square=4×sPerimeter\ of\ a\ Square = 4 \times s

Side of a Square=Perimeter4Side\ of\ a\ Square = \frac{Perimeter}{4}

Length of a Rectangle=Perimeter2−BreadthLength\ of\ a\ Rectangle = \frac{Perimeter}{2} - Breadth

Breadth of a Rectangle=Perimeter2−LengthBreadth\ of\ a\ Rectangle = \frac{Perimeter}{2} - Length

💡Examples

Problem 1:

Calculate the perimeter of a rectangular playground that has a length of 35 m35\ m and a breadth of 20 m20\ m.

Solution:

  1. Note the given dimensions: l=35 ml = 35\ m and b=20 mb = 20\ m.
  2. Apply the formula for the perimeter of a rectangle: P=2×(l+b)P = 2 \times (l + b).
  3. Substitute the values into the formula: P=2×(35+20)P = 2 \times (35 + 20).
  4. Add the values inside the brackets: P=2×55P = 2 \times 55.
  5. Multiply to find the final result: P=110 mP = 110\ m.

Explanation:

To find the total boundary of the playground, we add the length and the breadth to get the sum of two sides, then double it to account for all four sides.

Problem 2:

The perimeter of a square tile is 48 cm48\ cm. Find the length of each side of the tile.

Solution:

  1. Note the given perimeter: P=48 cmP = 48\ cm.
  2. Apply the formula to find the side of a square: s=P4s = \frac{P}{4}.
  3. Substitute the value: s=484s = \frac{48}{4}.
  4. Divide to find the side length: s=12 cms = 12\ cm.

Explanation:

Since all four sides of a square are equal, we divide the total perimeter (the distance around all four sides) by 4 to find the length of just one side.

Problem 3:

Find the perimeter of a square photo frame whose each side measures 15 cm15\ cm.

A square frame with side length 15 cm.

Solution:

Given: Side of the square (ss) = 15 cm15\ cm Formula: Perimeter=4×sPerimeter = 4 \times s Calculation: P=4×15P = 4 \times 15 P=60 cmP = 60\ cm

The perimeter of the photo frame is 60 cm60\ cm.

Explanation:

Since all four sides of a square are equal, we multiply the length of one side by 4 to get the total boundary length.

Problem 4:

The perimeter of a rectangular garden is 100 m100\ m. If its length is 30 m30\ m, find its breadth.

A rectangle representing a garden with length 30m and an unknown breadth.

Solution:

Given: Perimeter(P)=100 mPerimeter (P) = 100\ m Length(l)=30 mLength (l) = 30\ m Formula: Breadth=Perimeter2−LengthBreadth = \frac{Perimeter}{2} - Length Calculation: Half of Perimeter=1002=50 mHalf\ of\ Perimeter = \frac{100}{2} = 50\ m Breadth=50−30Breadth = 50 - 30 Breadth=20 mBreadth = 20\ m

The breadth of the garden is 20 m20\ m.

Explanation:

To find the breadth, we first find the sum of one length and one breadth (which is half the perimeter) and then subtract the known length.