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Perimeter and Area - Area

Grade 6CBSE

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

🔑Concepts

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Area is the amount of surface or region enclosed by a closed plane figure.

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The SI unit of area is square meters (m2m^2), but it can also be expressed in cm2cm^2 or mm2mm^2 depending on the dimensions.

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When calculating area using a squared paper or grid: count every full square as 11, every square that is more than half-filled as 11, every square that is exactly half-filled as 12\frac{1}{2}, and ignore squares that are less than half-filled.

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If the dimensions of a shape are given in different units, convert them to the same unit before calculating the area.

📐Formulae

Area of a Rectangle=l×bArea\ of\ a\ Rectangle = l \times b

Area of a Square=side×side=s2Area\ of\ a\ Square = side \times side = s^2

Length of a Rectangle=AreaBreadthLength\ of\ a\ Rectangle = \frac{Area}{Breadth}

Breadth of a Rectangle=AreaLengthBreadth\ of\ a\ Rectangle = \frac{Area}{Length}

💡Examples

Problem 1:

Find the area of a rectangle whose length is 15 cm15\ cm and breadth is 8 cm8\ cm.

Solution:

Area=l×bArea = l \times b Area=15×8=120 cm2Area = 15 \times 8 = 120\ cm^2

Explanation:

To find the area of a rectangle, we multiply the given length and breadth.

Problem 2:

What is the area of a square plot of land with a side of 12 m12\ m?

Solution:

Area=Side×SideArea = Side \times Side Area=12×12=144 m2Area = 12 \times 12 = 144\ m^2

Explanation:

Since all sides of a square are equal, the area is the side length squared.

Problem 3:

The area of a rectangular garden 50 m50\ m long is 300 sq. m300\ sq.\ m. Find the width of the garden.

Solution:

Width=AreaLengthWidth = \frac{Area}{Length} Width=30050=6 mWidth = \frac{300}{50} = 6\ m

Explanation:

The width (or breadth) of a rectangle can be found by dividing the total area by the known length.

Problem 4:

Find the cost of tiling a rectangular room of length 10 m10\ m and breadth 8 m8\ m at the rate of Rs 2020 per square meter.

Solution:

First, find the area: Area=10×8=80 m2Area = 10 \times 8 = 80\ m^2 Now, find the cost: Cost=80×20Cost = 80 \times 20 80×201600\begin{array}{r} 80 \\ \times 20 \\ \hline 1600 \end{array} The total cost is Rs 16001600.

Explanation:

Calculate the total area of the room first, then multiply the area by the rate per unit area to find the total cost.