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Mensuration - Area of a Square

Grade 6CBSE

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

🔑Concepts

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The area of a square is the total space or region enclosed within its four boundaries. In a square, all four sides are of equal length, and all interior angles are 90∘90^{\circ}.

A square with equal sides labeled 's' illustrating the area formula.
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To calculate the area, we multiply the length of one side by itself. The formula is written as: Area=side×sideArea = side \times side or Area=s2Area = s^2.

A square grid showing 2x2 units to visualize side squared.
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The units of area are always 'square units', such as cm2cm^2, m2m^2, or km2km^2. If a side is measured in cmcm, the area will be in sq cmsq\ cm.

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The relationship between side and area is such that if the side is doubled, the area becomes four times larger (2s×2s=4s22s \times 2s = 4s^2).

📐Formulae

Area of a Square=side×sideArea \text{ of a Square} = side \times side

Area=s2Area = s^2

Side=AreaSide = \sqrt{Area}

💡Examples

Problem 1:

Find the area of a square tile whose side length is 12cm12 cm.

Solution:

  1. Identify the side of the square: side=12cmside = 12 cm
  2. Write the formula for area: Area=side×sideArea = side \times side
  3. Substitute the value: Area=12cm×12cmArea = 12 cm \times 12 cm
  4. Calculate the result: Area=144cm2Area = 144 cm^2

Explanation:

To find the area, we simply multiply the side length by itself. The final unit is cm2cm^2 because we are multiplying two lengths measured in cmcm.

Problem 2:

A square playground has an area of 400m2400 m^2. What is the length of one side of the playground?

Solution:

  1. Given Area = 400m2400 m^2
  2. We know that Area=side×sideArea = side \times side
  3. So, side×side=400side \times side = 400
  4. We need to find a number which, when multiplied by itself, equals 400400. Since 20×20=40020 \times 20 = 400, then side=20mside = 20 m

Explanation:

When the area is provided, we perform the inverse operation of squaring (finding the square root) to determine the length of the side. We look for the number that squares to 400400.

Problem 3:

A square handkerchief has a side length of 25cm25 cm. Calculate the total area of the cloth used to make it.

A square representing a handkerchief with side labels of 25 cm.

Solution:

Given: Side of the square handkerchief (s)=25cm(s) = 25 cm Formula: Area=side×sideArea = side \times side Calculation: Area=25cm×25cmArea = 25 cm \times 25 cm Area=625cm2Area = 625 cm^2 The total area of the cloth is 625cm2625 cm^2.

Explanation:

We use the side length of 25cm25 cm and apply the square area formula by multiplying the side by itself.

Problem 4:

Find the cost of leveling a square plot of land with a side of 15m15 m at the rate of Rs 5050 per square meter.

A square plot of side 15m and calculated area 225 sq.m.

Solution:

Given: Side of the plot (s)=15m(s) = 15 m Rate of leveling = Rs 50/m250 / m^2 Step 1: Find the area of the plot. Area=15m×15m=225m2Area = 15 m \times 15 m = 225 m^2 Step 2: Calculate total cost. Total Cost=Area×RateTotal\ Cost = Area \times Rate Total Cost=225×50Total\ Cost = 225 \times 50 225×5011250\begin{array}{r} 225 \\ \times 50 \\ \hline 11250 \end{array} The total cost of leveling is Rs 11,25011,250.

Explanation:

First, the area is calculated using the side length. Then, the area is multiplied by the cost per unit area to find the total expense.