Steply

Converting area units

Geometry · 20 problems, easy to harder

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How we do it

  1. Change the length
  2. Change the area
  3. Multiply
  4. Check

The steps for Convert 3 m² to cm². Every solution names its steps, so you always know what comes next.

Worked examples

Convert 3 m² to cm² Easy

The question

Question: change 3 m² to square centimeters.

1 Change the length

This square is 1 meter on each side.

Its area is 1 square meter.

1 meter is 100 centimeters.

So each side is 100 centimeters long.

1 m = 100 cm

2 Change the area

So the square holds 100 rows of 100 small squares, each 1 square centimeter.

We draw only a few of them.

So 1 square meter is 100 centimeters times 100 centimeters.

1 m2 = 100 cm × 100 cm

100 times 100 is 10,000.

100 × 100 = 10,000

So 1 m² = 10,000 cm².

Not 100: the 100 comes in twice.

1 m2 = 10,000 cm2

3 Multiply

Each square meter is 10,000 square centimeters.

We have 3 of them, so we multiply: big unit to small unit.

3 m2 = 3 × 10,000 cm2

Careful!

Times 100 only changes a length.

A square has two sides to change: times 100, and times 100 again.

Careful: not 3 × 100 ✗

Times 10,000: write 4 zeros after 3.

× 10,000: the point moves 4 places right

So 3 m² = 30,000 cm².

3 m2 = 30,000 cm2

4 Check

Let's check: go back the other way.

Divide by 10,000.

30,000 ÷ 10,000 = 3

We get 3 square meters again.

So it is right!

Let's look back.

First: change the length.

Then: change the area.

Then: multiply.

Last: check.

Answer
3 m2 = 30,000 cm2

▶ Watch it solved

Convert 25000 cm² to m² Medium

The question

Question: change 25,000 cm² to square meters.

1 Change the length

This square is 1 meter on each side.

Its area is 1 square meter.

1 meter is 100 centimeters.

So each side is 100 centimeters long.

1 m = 100 cm

2 Change the area

So the square holds 100 rows of 100 small squares, each 1 square centimeter.

We draw only a few of them.

So 1 square meter is 100 centimeters times 100 centimeters.

1 m2 = 100 cm × 100 cm

100 times 100 is 10,000.

100 × 100 = 10,000

So 1 m² = 10,000 cm².

Not 100: the 100 comes in twice.

1 m2 = 10,000 cm2

3 Divide

10,000 square centimeters make 1 square meter.

So we divide by 10,000: small unit to big unit.

25,000 cm2 = 25,000 ÷ 10,000 m2

Careful!

Dividing by 100 only changes a length.

For square units it is 100 times 100: 10,000.

Careful: not 25,000 ÷ 100 ✗

Divided by 10,000: the point moves 4 places to the left.

÷ 10,000: the point moves 4 places left

So 25,000 cm² = 2.5 m².

25,000 cm2 = 2.5 m2

4 Check

Let's check: go back the other way.

Times 10,000.

2.5 × 10,000 = 25,000

We get 25,000 square centimeters again.

So it is right!

Let's look back.

First: change the length.

Then: change the area.

Then: divide.

Last: check.

Answer
25,000 cm2 = 2.5 m2

▶ Watch it solved

Convert 3000000 m² to km² Harder

The question

Question: change 3,000,000 m² to square kilometers.

1 Change the length

This square is 1 kilometer on each side.

Its area is 1 square kilometer.

1 kilometer is 1,000 meters.

So each side is 1,000 meters long.

1 km = 1,000 m

2 Change the area

So the square holds 1,000 rows of 1,000 small squares, each 1 square meter.

We draw only a few of them.

So 1 square kilometer is 1,000 meters times 1,000 meters.

1 km2 = 1,000 m × 1,000 m

1,000 times 1,000 is 1,000,000.

1,000 × 1,000 = 1,000,000

So 1 km² = 1,000,000 m².

Not 1,000: the 1,000 comes in twice.

1 km2 = 1,000,000 m2

3 Divide

1,000,000 square meters make 1 square kilometer.

So we divide by 1,000,000: small unit to big unit.

3,000,000 m2 = 3,000,000 ÷ 1,000,000 km2

Careful!

Dividing by 1,000 only changes a length.

For square units it is 1,000 times 1,000: 1,000,000.

Careful: not 3,000,000 ÷ 1,000 ✗

Divided by 1,000,000: the point moves 6 places to the left.

÷ 1,000,000: the point moves 6 places left

So 3,000,000 m² = 3 km².

3,000,000 m2 = 3 km2

4 Check

Let's check: go back the other way.

Times 1,000,000.

3 × 1,000,000 = 3,000,000

We get 3,000,000 square meters again.

So it is right!

Let's look back.

First: change the length.

Then: change the area.

Then: divide.

Last: check.

Answer
3,000,000 m2 = 3 km2

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. 3 m² to cm²
    Answer
    3 m2 = 30,000 cm2
  2. 5 m² to cm²
    Answer
    5 m2 = 50,000 cm2
  3. 2 ft² to in²
    Answer
    2 ft2 = 288 in2
  4. 4 yd² to ft²
    Answer
    4 yd2 = 36 ft2
  5. 6 cm² to mm²
    Answer
    6 cm2 = 600 mm2
  6. 10 m² to cm²
    Answer
    10 m2 = 100,000 cm2
  7. 2 km² to m²
    Answer
    2 km2 = 2,000,000 m2

Medium

  1. 25000 cm² to m²
    Answer
    25,000 cm2 = 2.5 m2
  2. 80000 cm² to m²
    Answer
    80,000 cm2 = 8 m2
  3. 288 in² to ft²
    Answer
    288 in2 = 2 ft2
  4. 45 ft² to yd²
    Answer
    45 ft2 = 5 yd2
  5. 700 mm² to cm²
    Answer
    700 mm2 = 7 cm2
  6. 2.5 m² to cm²
    Answer
    2.5 m2 = 25,000 cm2

Harder

  1. 3000000 m² to km²
    Answer
    3,000,000 m2 = 3 km2
  2. 0.5 m² to cm²
    Answer
    0.5 m2 = 5,000 cm2
  3. 1.5 ft² to in²
    Answer
    1.5 ft2 = 216 in2
  4. 4500 cm² to m²
    Answer
    4,500 cm2 = 0.45 m2
  5. how many cm² are in 7 m²
    Answer
    7 m2 = 70,000 cm2
  6. 3 yd² to in²
    Answer
    3 yd2 = 3,888 in2
  7. 1.2 km² to m²
    Answer
    1.2 km2 = 1,200,000 m2