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Measure - Introducing area (counting squares)

Grade 3Cambridge (IGCSE)

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

🔑Concepts

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Area is different from perimeter. While perimeter is the distance around the outside, area is the space filled inside. Using a grid is the easiest way to see this visually.

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To find the area of an irregular shape on a grid:

  1. Count all the full squares first.
  2. Look for half-squares and pair them up.
  3. Add the totals together.

📐Formulae

Area=Total number of unit squares\text{Area} = \text{Total number of unit squares}

Total Area=Full squares+(Half squares2)\text{Total Area} = \text{Full squares} + \left( \frac{\text{Half squares}}{2} \right)

💡Examples

Problem 1:

A rectangle is drawn on a grid. It covers 33 squares in its first row and has 44 rows in total. What is the area of the rectangle?

Solution:

We can count the squares row by row: Row 1: 33 squares Row 2: 33 squares Row 3: 33 squares Row 4: 33 squares Total=3+3+3+3=12\text{Total} = 3 + 3 + 3 + 3 = 12 The area is 1212 square units.

Explanation:

By counting the total number of unit squares that make up the rectangle, we find the total surface it covers.

Problem 2:

A triangle on a grid covers 66 full squares and 44 half-squares. What is the total area in cm2cm^2 if each square is 1 cm21\text{ cm}^2?

Solution:

  1. Count the full squares: 66
  2. Count the half-squares: 44
  3. Convert half-squares to full squares: 4÷2=2 full squares4 \div 2 = 2\text{ full squares}
  4. Add them together: Area=6+2=8 cm2\text{Area} = 6 + 2 = 8\text{ cm}^2

Explanation:

Since two halves make a whole, 44 halves are equal to 22 whole squares. Adding these to the 66 full squares gives the total area.

Problem 3:

Calculate the area of a shape that covers these squares: 5 full squares+2 half squaresTotal squares\begin{array}{r} 5 \text{ full squares} \\ + 2 \text{ half squares} \\ \hline \text{Total squares} \end{array}

Solution:

The 22 half squares combine to make 11 full square. Area=5+1=6 square units\text{Area} = 5 + 1 = 6\text{ square units}

Explanation:

We simplify the half-squares first and then add the result to the count of whole squares.

Introducing area (counting squares) Grade 3 Notes & Examples