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Introducing area

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visibility 70update 2 months agobookmarkshare

🎯 In this topic you will

Draw straight lines, rectangles, and squares accurately.
Estimate, measure, and calculate perimeters and areas of shapes.

🧠 Key Words

area
square units

Show Definitions

area: The amount of space inside a flat shape or surface.
square units: Units used to measure area, based on counting how many equal squares cover a surface completely.

📐 What Is Area?

I n this section you will learn about area. Area is the amount of space that a shape covers.

📏 Area vs Perimeter

Y ou will also do more work on perimeters and find the differences between area and perimeter.

🔷 Types of Shapes

T his section uses both regular and irregular shapes to help you practise measuring and comparing areas and perimeters.

📘 Worked example

Sofia and Zara are talking about area.

Sofia says the area of the square is 4 square units because it contains four small squares.

Zara says the square has four sides, each side is two squares long, so she adds $2 + 2 + 2 + 2 = 8$ square units.

Who is right?

Answer:

Sofia is right. The area is how much space a shape covers. This square covers four unit squares, so the area is $4$ square units.

Zara is incorrect because she is counting around the outside of the square. She is finding the perimeter, not the area.

To find area, count how many equal squares fit inside the shape.

To find perimeter, add the lengths of all the sides around the shape.

Here, counting the four inside squares gives the area ($4$ square units), while adding the sides gives the perimeter ($8$ units).

❓ EXERCISES

$1.$ Estimate, measure and calculate the area of these shapes.

Write the area on the shape and the estimate below the shape.

👀 Show answer

a. Area $= 25$ square units.

b. Area $= 25$ square units.

c. Area $= 4$ square units.

d. Area $= 7$ square units.

Estimates should be close to these values.

$2.$ Do you think that these shapes have the same area? Check and find out.

Make some more shapes that have the same area but look different. Record them on squared paper.

👀 Show answer

Yes. Counting the unit squares shows both shapes cover the same total number of squares, so they have equal area even though they look different.

Many different shapes can be drawn using the same number of square units.

$3.$

a. If the area of a square is $81$ square units, how long are the sides?

b. What is the perimeter? Show how you know.

👀 Show answer

a. Each side is $\sqrt{81} = 9$ units.

b. Perimeter $= 4 \times 9 = 36$ units.

🧠 Think like a Mathematician

Thandiwe says, “All rectangles with a perimeter of $26$ metres will have the same area.”

a. Is he right? How can you find out?

b. Explain how you know.

👀 show answer

a. No, he is not right. You can test this by drawing several rectangles that all have perimeter $26$ m (for example $6 \times 7$, $5 \times 8$, $4 \times 9$) and then calculating each area.
b. Although the perimeter stays the same, the areas are different. For example:
$6 \times 7 = 42$, $5 \times 8 = 40$, $4 \times 9 = 36$.
This shows rectangles with the same perimeter can have different areas, so Thandiwe’s statement is false.

📘 What we've learned

We learned how to draw straight lines, rectangles, and squares accurately.
We practised estimating, measuring, and calculating perimeters and areas.
We learned that area means how much space a shape covers, measured in square units.
We learned that perimeter is the total distance around a shape.
The area of a rectangle is found using $\text{Area} = \text{length} \times \text{width}$.
The perimeter of a rectangle is found using $\text{Perimeter} = 2(\text{length} + \text{width})$.
We explored how shapes can have the same perimeter but different areas.

Introducing area

🎯 In this topic you will

🧠 Key Words

📐 What Is Area?

📏 Area vs Perimeter

🔷 Types of Shapes

❓ EXERCISES

🧠 Think like a Mathematician

📘 What we've learned

Related Past Papers

Related Tutorials

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