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Mensuration - Area of a Rectangle

Grade 6CBSE

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

🔑Concepts

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The area of a rectangle is the measure of the total surface or region enclosed within its four boundaries. It is calculated by multiplying its two dimensions: length (ll) and breadth (bb).

A rectangle showing length and breadth dimensions.
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Area is always expressed in square units, such as cm2\text{cm}^2, m2\text{m}^2, or km2\text{km}^2. If the dimensions are in different units, they must be converted to the same unit before calculating the area.

A unit square representing 1 square unit of area.
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If the total area and one dimension (either length or breadth) are known, the missing dimension can be found by dividing the area by the known dimension.

Conceptual diagram showing how to derive length from area.
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When calculating the area of complex shapes, we can often divide the shape into smaller rectangles, calculate their individual areas, and then add them together.

📐Formulae

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

A=l×bA = l \times b

Length(l)=AreaBreadth\text{Length} (l) = \frac{\text{Area}}{\text{Breadth}}

Breadth(b)=AreaLength\text{Breadth} (b) = \frac{\text{Area}}{\text{Length}}

1 m2=10,000 cm21\text{ m}^2 = 10,000\text{ cm}^2

💡Examples

Problem 1:

A rectangular park has a length of 15 m15\text{ m} and a breadth of 8 m8\text{ m}. Calculate the total area of the park.

Solution:

Given:\nLength (ll) = 15 m15\text{ m}\nBreadth (bb) = 8 m8\text{ m}

Using the formula: Area=l×b\text{Area} = l \times b Area=15 m×8 m\text{Area} = 15\text{ m} \times 8\text{ m} Area=120 sq m\text{Area} = 120\text{ sq m}

Explanation:

To find the area, we multiply the two given dimensions. Since both dimensions are in meters, the final unit is square meters (sq m\text{sq m}).

Problem 2:

The area of a rectangular table top is 2400 sq cm2400\text{ sq cm}. If the length of the table is 60 cm60\text{ cm}, find its breadth.

Solution:

Given:\nArea (AA) = 2400 sq cm2400\text{ sq cm}\nLength (ll) = 60 cm60\text{ cm}

Using the formula for breadth: b=Alb = \frac{A}{l} b=240060b = \frac{2400}{60} b=40 cmb = 40\text{ cm}

Explanation:

To find the missing dimension (breadth), we divide the total area by the given length. Since the area is in sq cm\text{sq cm} and length is in cm\text{cm}, the breadth will be in cm\text{cm}.

Problem 3:

A rectangular playground has a length of 40 m40\text{ m} and its breadth is half of its length. Find the area of the playground.

Rectangle with length 40m and breadth 20m.

Solution:

Given: Length (ll) = 40 m40\text{ m} Breadth (bb) = 12×Length=12×40=20 m\frac{1}{2} \times \text{Length} = \frac{1}{2} \times 40 = 20\text{ m}

Area of Rectangle=l×b\text{Area of Rectangle} = l \times b Area=40 m×20 m\text{Area} = 40\text{ m} \times 20\text{ m} Area=800 m2\text{Area} = 800\text{ m}^2

The area of the playground is 800 sq m800\text{ sq m}.

Explanation:

First, we determine the breadth by taking half of the given length. Then, we apply the standard area formula for a rectangle.

Problem 4:

A room has a rectangular floor of length 5 m5\text{ m} and breadth 4 m4\text{ m}. A square carpet of side 3 m3\text{ m} is laid on the floor. Find the area of the floor that is NOT carpeted.

A rectangle representing a room floor with a smaller square carpet inside.

Solution:

Step 1: Calculate total floor area. Area of floor=5 m×4 m=20 m2\text{Area of floor} = 5\text{ m} \times 4\text{ m} = 20\text{ m}^2

Step 2: Calculate area of the square carpet. Area of carpet=3 m×3 m=9 m2\text{Area of carpet} = 3\text{ m} \times 3\text{ m} = 9\text{ m}^2

Step 3: Calculate uncarpeted area. Uncarpeted Area=Total Floor Area−Carpet Area\text{Uncarpeted Area} = \text{Total Floor Area} - \text{Carpet Area} 20−911\begin{array}{r} 20 \\ - 9 \\ \hline 11 \end{array}

The area of the floor not covered by the carpet is 11 m211\text{ m}^2.

Explanation:

To find the remaining area, we subtract the area of the smaller shape (carpet) from the area of the larger rectangular shape (floor).