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Perimeter, Area and Volume - Area of Square and Rectangle

Grade 5ICSE

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

🔑Concepts

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The area of a square is the amount of surface covered by it. Since all sides are equal in a square, we multiply the side by itself to find the area: Area=side×side=side2\text{Area} = \text{side} \times \text{side} = \text{side}^2

A square with side 's' representing area as s times s.
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The area of a rectangle is calculated by multiplying its length by its breadth. If the area and one dimension are known, the missing dimension can be found using: Length=AreaBreadth\text{Length} = \frac{\text{Area}}{\text{Breadth}} or Breadth=AreaLength\text{Breadth} = \frac{\text{Area}}{\text{Length}}

A rectangle showing length and breadth labels.
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Area is always measured in square units, such as cm2cm^2, m2m^2, or km2km^2. It represents the number of unit squares that fit inside a shape.

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When calculating area, ensure that both the length and breadth are in the same unit. If they are different (e.g., one in mm and one in cmcm), convert them to a common unit before multiplying.

📐Formulae

Area of a Rectangle=Length×Breadth\text{Area of a Rectangle} = \text{Length} \times \text{Breadth}

Area of a Square=Side×Side\text{Area of a Square} = \text{Side} \times \text{Side}

Length of a Rectangle=AreaBreadth\text{Length of a Rectangle} = \frac{\text{Area}}{\text{Breadth}}

Breadth of a Rectangle=AreaLength\text{Breadth of a Rectangle} = \frac{\text{Area}}{\text{Length}}

Side of a Square=Area\text{Side of a Square} = \sqrt{\text{Area}}

💡Examples

Problem 1:

A rectangular room has a length of 12 m12\ m and a breadth of 8 m8\ m. Find the area of the floor.

Solution:

Given: Length (LL) = 12 m12\ m Breadth (BB) = 8 m8\ m

Using the formula: Area=L×B\text{Area} = L \times B Area=12 m×8 m\text{Area} = 12\ m \times 8\ m Area=96 m2\text{Area} = 96\ m^2

Explanation:

To find the area of the rectangular floor, we multiply the given length by the breadth. The result is expressed in square meters because the dimensions were in meters.

Problem 2:

Find the area of a square tile whose side measures 15 cm15\ cm.

Solution:

Given: Side (SS) = 15 cm15\ cm

Using the formula: Area=S×S\text{Area} = S \times S Area=15 cm×15 cm\text{Area} = 15\ cm \times 15\ cm Area=225 cm2\text{Area} = 225\ cm^2

Explanation:

Since all sides of a square are equal, we calculate the area by multiplying the side length by itself. The final answer is in square centimeters.

Problem 3:

A rectangular garden has an area of 300 m2300\ m^2. If the length of the garden is 20 m20\ m, find its breadth.

Rectangle with area 300 and length 20, breadth marked with a question mark.

Solution:

Given: Area of the rectangle = 300 m2300\ m^2 Length = 20 m20\ m

Formula: Breadth=AreaLength\text{Breadth} = \frac{\text{Area}}{\text{Length}}

Calculation: Breadth=30020 m\text{Breadth} = \frac{300}{20}\ m Breadth=15 m\text{Breadth} = 15\ m

The breadth of the garden is 15 m15\ m.

Explanation:

To find the missing breadth of a rectangle when the area and length are given, divide the area by the known length.

Problem 4:

Find the area of a square park if its perimeter is 64 m64\ m.

Square with perimeter 64 m and calculated side of 16 m.

Solution:

Given: Perimeter of the square = 64 m64\ m

Step 1: Find the side of the square. Side=Perimeter4\text{Side} = \frac{\text{Perimeter}}{4} Side=644=16 m\text{Side} = \frac{64}{4} = 16\ m

Step 2: Find the area. Area=Side×Side\text{Area} = \text{Side} \times \text{Side} Area=16×16=256 m2\text{Area} = 16 \times 16 = 256\ m^2

The area of the square park is 256 m2256\ m^2.

Explanation:

First, use the perimeter to find the length of one side by dividing by 4. Then, square that side length to find the area.