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Convert Metric Units of Area

In this worksheet, students will practise converting areas into alternative units of measurement by applying the area conversion factor.

Worksheet Overview

QUESTION 1 of 10

You may be familiar with converting between different units (e.g. m and cm, or m and km), but how do we apply this when we are also calculating areas

 

 

When we are converting from, for example, metres into cm, we know that 1 m = 100 cm.

This can lead to the misconception that 1 m2 = 100 cm2.

BUT, in reality, 1 m2 = 10000 cm2 as we need to take into account our area conversion factors

 

Let's look at what we mean here with a diagram to help. 

 

If we look at a square that measures 1 m on each side:

 

Looking at the areas of these two identical squares, we can say that:

1 m × 1 m = 100 cm × 100 cm

1 m2 = 10000 cm2

 

Is there a trick?

In a way, yes.

All we need to do for an area conversion is to find the conversion if it was a length, and then square it to get the area conversion.

 

 

 

Let's look at an example to see this in action.

 

 

e.g. Convert 1.4 m2 into cm2.

 

We know that for length, 1 m = 100 cm.

So for area, 1 m2 = 10000 cm2.

So 1.4 m2 = 1.4 × 10000 = 14000 cm2.

 

 

 

e.g. Convert 350 m2 into km2.

 

We know that for a length, 1 km = 1000 m.

So for area, 1 km2 = 1000000 m2.

So 350 m2 = 350 ÷ 1000000 = 0.00035 m2.

 

 

 

In this activity, we will convert areas (expressed in cm2, m2 and km2) into alternative units of measurement by applying the area conversion factor using the methods shown above. 

Type a number into the space to complete the sentence below. 

Type a word into the space to complete the sentence below.

Type a word into the first space and a number into the second space to complete the sentence below.

What is 175 cm2 converted into m2?

1,750,000 m2

0.0175 m2

175,000 m2

What is 4.2 km2 converted into m2?

4,200,000 m2

0.0000042 m2

420,000 m2

State if each conversion below is correct or not by selecting either the 'Correct' or 'Incorrect' option. 

Convert 4.1 m2 into cm2.

 

Type your answer as only a number below, as the units have already been provided for you. 

Convert 354 cm2 into m2.

 

Type your answer as only a number below, as the units have already been provided for you. 

Convert 4.1 km2 into m2.

 

Type your answer as only a number below, as the units have already been provided for you. 

Convert 2,950,000 m2 into km2.

 

Type your answer as only a number below, as the units have already been provided for you. 

  • Question 1

Type a number into the space to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
We know that 1 m = 100 cm. If we square these numbers to find the area conversion factor, we reach 10000. So 1 m2 = 10,000 cm2
  • Question 2

Type a word into the space to complete the sentence below.

CORRECT ANSWER
EDDIE SAYS
This is the opposite of the previous statement. To move from cm2 to m2, we needed to divide, so to do the opposite, and move from m2 to cm2, we need to multiply. Does that make sense?
  • Question 3

Type a word into the first space and a number into the second space to complete the sentence below.

CORRECT ANSWER
EDDIE SAYS
We know that 1 km = 1000 m. If we square these numbers to find the area conversion factor, we reach 1,000,000. So 1 km2 = 10,000 m2 As metres are smaller than kilometres, we will need to have more of them to express the same value, so we need to multiply them.
  • Question 4

What is 175 cm2 converted into m2?

CORRECT ANSWER
0.0175 m2
EDDIE SAYS
Firstly, we need to find our conversion factor: 1 m = 100 cm So 1 m2 = 1002 = 10,000 cm2 Because a m2 is bigger than a cm2, we will have less of them, so we must divide: 175 ÷ 10000 = 0.0175 m2
  • Question 5

What is 4.2 km2 converted into m2?

CORRECT ANSWER
4,200,000 m2
EDDIE SAYS
Let's find our conversion factor: 1 km = 1000 m So 1 km2 = 10002 = 1,000,000 m2 Because a m2 is smaller than a km2, we will have more of them, so we must multiply: 4.2 × 1000000 = 4200000 m2
  • Question 6

State if each conversion below is correct or not by selecting either the 'Correct' or 'Incorrect' option. 

CORRECT ANSWER
EDDIE SAYS
Did you remember to square the conversion factors here? Let's take each conversion one at a time, and see if the answer we reach matches the value provided. cm2 > m2 = 1002 = 10000 m2 are larger than cm2 so there will be less, and we need to divide to achieve this: 1500 ÷ 10000 = 0.15 m2 This does not match the answer provided so the first conversion is incorrect. cm2 > m2 = 10000 cm2 are smaller than m2 so there will be more, and we need to multiply to achieve this: 1.5 × 10000 = 15000 cm2 This does match the answer provided so the second conversion is correct. km2 > m2 = 10002 = 1000000 m2 are smaller than km2 so there will be more, and we need to multiply to achieve this: 1.5 × 1000000 = 1500000 m2 This also does not match the answer provided so the final conversion is incorrect too. Did you identify the single correct conversion here?
  • Question 7

Convert 4.1 m2 into cm2.

 

Type your answer as only a number below, as the units have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
Remember to square the length conversion here: 1 m = 100 cm So 1 m2 = 10000 cm2 As centimetres are smaller than metres, we should have more of them. To achieve this, we need to multiply: 4.1 × 10000 = 41,000 cm2
  • Question 8

Convert 354 cm2 into m2.

 

Type your answer as only a number below, as the units have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
1 m = 100 cm 1 m2 = 10000 cm2 As metres are larger than metres, we should have less of them. To achieve this, we need to divide: 354 ÷ 10000 = 0.0354 m2 Well done if you spotted that this was the inverse operation of the previous question.
  • Question 9

Convert 4.1 km2 into m2.

 

Type your answer as only a number below, as the units have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
1 km = 1000 m So 1 km2 = 1000000 m2 As metres are smaller than kilometres, we should have more of them. To achieve this, we need to multiply: 4.1 × 1000000 = 4,100,000 m2
  • Question 10

Convert 2,950,000 m2 into km2.

 

Type your answer as only a number below, as the units have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
1 km = 1000 m So 1 km2 = 1000000 m2 As kilometres are larger than metres, we should have less of them. To achieve this, we need to divide: 2950000 × 1000000 = 2.95 km2 You can now convert area amounts into different units by finding the area conversion factor and deciding whether to multiply or divide - nice work!
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