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Area and Perimeter - Area of Rectangles and Squares

Grade 5CBSE

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

🔑Concepts

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The area of a rectangle is the amount of surface it covers. It is calculated by multiplying the length of the rectangle by its breadth. The unit is always in square units like cm2cm^2 or m2m^2.

A rectangle showing length and breadth labels.
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A square is a special type of rectangle where all four sides are equal. Therefore, the area is simply the side multiplied by itself: Area=side×sideArea = side \times side.

A square with equal sides labeled.
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To find a missing dimension when the area is known, use division. If you know the area and breadth of a rectangle, length=Area÷breadthlength = Area \div breadth.

Rectangle with area 48, breadth 6, and unknown length.
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Standard units of area include square millimeters (mm2mm^2), square centimeters (cm2cm^2), and square meters (m2m^2). Remember that 1 m2=10,000 cm21\ m^2 = 10,000\ cm^2 because 100 cm×100 cm=10,000 cm2100\ cm \times 100\ cm = 10,000\ cm^2.

📐Formulae

Area of a Rectangle=length×breadthArea\ of\ a\ Rectangle = length \times breadth

Area of a Square=side×sideArea\ of\ a\ Square = side \times side

length=Areabreadthlength = \frac{Area}{breadth}

breadth=Arealengthbreadth = \frac{Area}{length}

1 cm2=100 mm21\ cm^2 = 100\ mm^2

1 m2=10,000 cm21\ m^2 = 10,000\ cm^2

💡Examples

Problem 1:

A rectangular playground has a length of 25 m25\ m and a breadth of 12 m12\ m. Calculate the total area of the playground.

Solution:

Step 1: Identify the given dimensions: length=25 mlength = 25\ m and breadth=12 mbreadth = 12\ m. \nStep 2: Use the formula for the area of a rectangle: Area=length×breadthArea = length \times breadth. \nStep 3: Substitute the values into the formula: Area=25×12Area = 25 \times 12. \nStep 4: Perform the multiplication: 25×12=30025 \times 12 = 300. \nStep 5: State the final answer with the correct units: Area=300 m2Area = 300\ m^2.

Explanation:

To find the surface space of the rectangle, we multiply the two primary dimensions (length and breadth) together.

Problem 2:

The area of a square photo frame is 144 cm2144\ cm^2. Find the length of each side of the frame.

Solution:

Step 1: Identify the given information: Area=144 cm2Area = 144\ cm^2. \nStep 2: Recall the formula for the area of a square: Area=side×sideArea = side \times side. \nStep 3: Find a number that, when multiplied by itself, equals 144144. \nStep 4: Since 12×12=14412 \times 12 = 144, the side must be 1212. \nStep 5: State the final answer: side=12 cmside = 12\ cm.

Explanation:

In a square, all sides are equal. To find the side length from the area, we look for the square root of the area value.

Problem 3:

A square garden has a side length of 15 m15\ m. Find the area of the garden.

A square with sides of 15m.

Solution:

Given: Side of the square garden = 15 m15\ m Formula: Area=side×sideArea = side \times side Calculation: Area=15 m×15 mArea = 15\ m \times 15\ m Area=225 m2Area = 225\ m^2

The area of the garden is 225 m2225\ m^2.

Explanation:

To find the area of a square, we multiply the side by itself. Since the side is 15 m15\ m, we calculate 15×1515 \times 15.

Problem 4:

The area of a rectangular carpet is 120 cm2120\ cm^2. If the breadth of the carpet is 8 cm8\ cm, find its length.

A rectangle with area 120 and breadth 8.

Solution:

Given: Area=120 cm2Area = 120\ cm^2 Breadth=8 cmBreadth = 8\ cm Formula: Length=AreaBreadthLength = \frac{Area}{Breadth} Calculation: Length=1208Length = \frac{120}{8} Length=15 cmLength = 15\ cm

The length of the carpet is 15 cm15\ cm.

Explanation:

When the area and one dimension (breadth) are given, we divide the area by the breadth to find the other dimension (length).