Practice Maths

Area Units and Conversion

Key Ideas

Key Terms

area unit
the unit used to measure area; always squared because area is two-dimensional (e.g. mm², cm², m², km², ha).
square millimetre (mm²)
the area of a 1 mm × 1 mm square; used for very small objects.
square centimetre (cm²)
the area of a 1 cm × 1 cm square; 1 cm² = 100 mm².
square metre (m²)
the area of a 1 m × 1 m square; 1 m² = 10 000 cm².
square kilometre (km²)
the area of a 1 km × 1 km square; 1 km² = 1 000 000 m² = 100 ha.
hectare (ha)
a unit of land area equal to 10 000 m²; a square 100 m × 100 m; 1 km² = 100 ha.

Converting area units

To convert to a smaller unit, multiply by the conversion factor.
To convert to a larger unit, divide by the conversion factor.

Hot Tip For area conversions, always square the linear factor. Since 1 m = 100 cm, we get 1 m² = 100² cm² = 10 000 cm². Don’t just multiply by 100 — multiply by 10 000!

Worked Example

Question: Convert 3.5 m² to cm².

Step 1 — Identify the conversion factor.
1 m² = 10 000 cm²

Step 2 — Multiply (going to smaller units).
3.5 × 10 000 = 35 000 cm²

1 m² = 10 000 cm² (100 cm × 100 cm) 1 m 1 m = 100 cm → ×100² = ×10 000 m² → cm² ÷10 000 cm² → m²

The Units of Area

Area measures the amount of surface inside a shape. Because area is two-dimensional, its units are always squared: mm2, cm2, m2, km2. We also use hectares (ha) for land area.

Think of each unit as a tiny square tile. 1 cm2 is a square that is 1 cm by 1 cm. 1 m2 is a square that is 1 m by 1 m (about the size of a large floor tile). 1 km2 is a square that is 1 km by 1 km — big enough to fit many suburbs inside it.

1 hectare = 10 000 m2 (about the size of a sporting oval or a rugby league field plus surroundings). Land and farms are measured in hectares.

Why Area Conversions Use Squared Factors

Here's where many students get confused. When converting length, you multiply or divide by 10, 100, or 1 000. But for area, you square those factors.

Think about it: a square with sides 1 cm = 10 mm on each side. Its area = 10 × 10 = 100 mm2. So 1 cm2 = 100 mm2 (not 10 mm2).

A square with sides 1 m = 100 cm. Area = 100 × 100 = 10 000 cm2. So 1 m2 = 10 000 cm2.

A square 1 km = 1 000 m on each side. Area = 1 000 × 1 000 = 1 000 000 m2. So 1 km2 = 1 000 000 m2.

The Full Conversion Chain

Here is the complete chain of area unit conversions:

1 cm2 = 100 mm2   (multiply by 100 to go from cm2 to mm2)
1 m2 = 10 000 cm2   (multiply by 10 000 to go from m2 to cm2)
1 ha = 10 000 m2   (multiply by 10 000 to go from ha to m2)
1 km2 = 1 000 000 m2   (multiply by 1 000 000 to go from km2 to m2)
1 km2 = 100 ha

To convert to a smaller unit, multiply. To convert to a larger unit, divide.

Worked Conversion Examples

Example 1: Convert 3.5 m2 to cm2.
3.5 × 10 000 = 35 000 cm2

Example 2: Convert 250 000 m2 to hectares.
250 000 ÷ 10 000 = 25 ha

Example 3: Convert 4.2 km2 to hectares.
4.2 × 100 = 420 ha

Example 4: A bedroom floor measures 12 m2. How many cm2 is this?
12 × 10 000 = 120 000 cm2

Choosing the Right Unit

Choosing the appropriate unit makes your answer meaningful. You wouldn't express the area of a farm in mm2 (the number would be astronomically large) or the area of a fingernail in km2 (impossibly small). Match the scale of the measurement to the unit:

• Tiny objects (stamps, coins): mm2
• Rooms, buildings, school grounds: m2
• Farms, parks, suburbs: ha or km2
• Countries, states: km2

Key tip: When converting area units, square the length conversion factor. Since 1 m = 100 cm, then 1 m2 = 1002 cm2 = 10 000 cm2. Students who forget to square the factor and use 100 instead of 10 000 will get answers that are 100 times too small. Always square it!

Mastery Practice

  1. Convert each measurement between mm² and cm². Fluency

    1. 4 cm² = ___ mm²
    2. 700 mm² = ___ cm²
    3. 12.5 cm² = ___ mm²
    4. 350 mm² = ___ cm²
    5. 0.8 cm² = ___ mm²
    6. 2500 mm² = ___ cm²
    7. 9 cm² = ___ mm²
    8. 48 mm² = ___ cm²

  2. Convert each measurement between cm² and m². Fluency

    1. 2 m² = ___ cm²
    2. 50 000 cm² = ___ m²
    3. 0.75 m² = ___ cm²
    4. 8 400 cm² = ___ m²
    5. 3.5 m² = ___ cm²
    6. 125 000 cm² = ___ m²
    7. 0.04 m² = ___ cm²
    8. 960 cm² = ___ m²

  3. Convert between hectares, m² and km². Fluency

    1. 3 ha = ___ m²
    2. 250 000 m² = ___ ha
    3. 1.5 km² = ___ ha
    4. 450 ha = ___ km²
    5. 0.6 ha = ___ m²
    6. 80 000 m² = ___ ha
    7. 2.8 km² = ___ m²
    8. 500 ha = ___ km²

  4. Choose the most appropriate unit (mm², cm², m², ha, or km²) for each situation. Give a reason. Understanding

    1. The area of a fingernail
    2. The area of a school oval
    3. The area of Queensland
    4. The area of a bedroom floor
    5. The area of a postage stamp
    6. The area of a cattle station
    7. The area of a computer screen
    8. The area of a national park

  5. Solve each problem, showing all working and units at each step. Problem Solving

    1. An architect draws a floor plan. One room measures 450 cm by 320 cm on the plan.
      1. Calculate the area of the room in cm².
      2. Convert this area to m².
      3. The homeowner wants to tile the floor. Tiles cost $45 per m². How much will tiling cost?
    2. A wheat farm covers 2 800 ha.
      1. Convert 2 800 ha to km².
      2. The farm is divided into equal paddocks. If each paddock is 35 ha, how many paddocks are there?
      3. One paddock produces 3.2 tonnes of wheat per ha. How many tonnes does one paddock produce?
    3. A tile is a square with side length 20 cm.
      1. Find the area of one tile in cm².
      2. Convert the tile area to mm².
      3. How many tiles are needed to cover a floor area of 7.2 m²? (Ignore grout gaps.)

  6. Order each set of areas from smallest to largest. Convert to the same unit to compare. Understanding

    1. 5 cm², 450 mm², 0.0005 m²
    2. 2 ha, 18 000 m², 0.025 km²
    3. 1 m², 9 500 cm², 0.00012 km²
    4. 300 mm², 2.9 cm², 0.000028 m²
    5. 0.5 ha, 4 800 m², 0.006 km²
    6. 1 km², 95 ha, 1 100 000 m²

  7. State whether each statement is true or false. If false, correct it. Understanding

    1. 1 m² = 1000 cm²
    2. To convert from m² to cm², you multiply by 100.
    3. 1 ha = 10 000 m²
    4. 2.5 km² = 250 ha
    5. 50 000 cm² = 5 m²
    6. The conversion factor from km² to m² is 1 000 000.
    7. A 1 km × 1 km square has an area of 100 ha.
    8. To convert cm² to mm², multiply by 10.

  8. Extended response: Show all working, convert units at each step, and write a conclusion sentence. Problem Solving

    1. A solar panel is rectangular with length 1.65 m and width 0.99 m.
      1. Find the area of one panel in m² (to 4 dp).
      2. Convert this area to cm².
      3. A household roof can fit 18 solar panels. Find the total panel area in m².
    2. A national park covers 34 800 ha.
      1. Express this area in km².
      2. Express this area in m² (use scientific notation).
      3. A ranger patrols a circular section of the park. If the circular section has an area of 12 000 m², what percentage of the total park area is this? Round to 4 decimal places.
    3. A tiler is choosing between two tile options for a bathroom floor of area 8.4 m²:
      • Option A: square tiles with side 20 cm, sold in boxes of 10 at $22 per box
      • Option B: rectangular tiles 40 cm × 25 cm, sold in boxes of 8 at $26 per box
      1. Find the area of one tile for each option (in cm² and m²).
      2. Find the number of boxes required for each option (assume 10% extra for wastage).
      3. Find the total cost for each option and decide which is cheaper.

  9. Use the conversion chain below to fill in each missing value. Understanding

    mm² ×100 ÷100 cm² ×10 000 ÷10 000 m² ×1 000 000 ÷1 000 000 km²
    1. 500 cm² = ___ mm²
    2. 3.6 m² = ___ cm²
    3. 4 500 000 m² = ___ km²
    4. 0.002 km² = ___ m²
    5. 75 000 cm² = ___ m²
    6. 2 800 mm² = ___ cm²

  10. Spot the error: Each student made a mistake converting areas. Identify the error and give the correct answer. Problem Solving

    1. Student A: “2 m² = 200 cm² because 1 m = 100 cm.”
    2. Student B: “5 ha = 500 m² because I divided by 10.”
    3. Student C: “1 km² = 1000 m² because 1 km = 1000 m.”
    4. Student D: “30 mm² = 3 cm² because I divided by 10.”
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