Units of Area
Table Of Contents
🎬 Math Angel Video: Converting Units of Area
What Is Area?
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🛎️ 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.
What Are Units of Area?
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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 pencil1 cm² (square centimeter): a square that’s 1 cm by 1 cm
→ Used for small surfaces, like a calculator screen1 m² (square meter): a square that’s 1 m by 1 m
→ Used for measuring rooms, floors, walls1 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.
How to Convert Between Units of Area?
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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:
$1\,\text{cm}^2 = 100\,\text{mm}^2$
$1\,\text{m}^2 = 10,\!000\,\text{cm}^2$
$1\,\text{km}^2 = 1,\!000,\!000\,\text{m}^2$
Converting Area Units (Examples)
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🛎️ 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: $5,000 \div 100 = 50\,\text{cm}^2$
🍪 Quiz (6 Questions): Practice Converting Area Units
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