Units of Area

🌟 Definition of Area:

Area is the amount of space a flat surface covers.

It tells us how many square units fit inside a shape.

🌟 Understanding Area with an Example:

For example, we can use unit squares with sides of 1 meter to measure the size of a room.

If a room can fit 25 of such squares on the floor, then the room has an area of:

$$25 \times 1\, \text{m}^2 = 25\, \text{m}^2$$

So, the area of the room is 25 square meters.

Units of area are measurements used to describe area.

Each unit is a square with sides of equal length.

🌟 Common Units of Area:

• 1 mm² (square millimeter): a square that’s 1 mm by 1 mm
  → Used for tiny objects, like the tip of a pencil

• 1 cm² (square centimeter): a square that’s 1 cm by 1 cm
  → Used for small surfaces, like a calculator screen

• 1 m² (square meter): a square that’s 1 m by 1 m
  → Used for measuring rooms, floors, walls

• 1 km² (square kilometer): a square that’s 1 km by 1 km
  → Used for very large areas, like cities or parks

✅ Exam Tip: The unit you choose depends on the size of what you’re measuring. Use mm² or cm² for small things, and m² or km² for bigger areas.

When converting area, you square the length conversion factor.

🌟 Example: Converting cm² to mm²

We know:
$1\,\text{cm} = 10\,\text{mm}$

So:
$1\,\text{cm}^2 = 1\,\text{cm} \times 1\,\text{cm} = 10\,\text{mm} \times 10\,\text{mm} = 100\,\text{mm}^2$

🌟 How to Convert Area Units:

• To convert to a smaller unit, multiply:

• To convert to a larger unit, divide:
  

  • $1\,\text{cm}^2 = 100\,\text{mm}^2$

  • $1\,\text{m}^2 = 10,\!000\,\text{cm}^2$

  • $1\,\text{km}^2 = 1,\!000,\!000\,\text{m}^2$

🔍 Example 1: Convert 3 m² to cm²

We know:
$1\,\text{m}^2 = 10,000\,\text{cm}^2$

When converting to a smaller unit, multiply.
So: $3 \times 10,000 = 30,000\,\text{cm}^2$

🔍 Example 2: Convert 5,000 mm² to cm²

We know:
$1\,\text{cm}^2 = 100\,\text{mm}^2$

When converting to a larger unit, divide.
So: $5,000 \div 100 = 50\,\text{cm}^2$