 # Area of a Square

In this worksheet students will learn the formula for finding the area of a square and be able to find areas. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation, Area Calculations

Difficulty level:   ### QUESTION 1 of 10

The good old square.

They have been around us since forever.

Its most probably the first shape you were taught to recognise. What examples can you think of that we see in everyday life? I have just cut my lawn and it got me to think about the area of squares.

There are all sorts of reasons we may need to know the area of a square.

Laying a carpet in a square room, painting a square wall, putting grass seed over a square lawn.

Before we can do any of this there is one thing we need to know and that is how to find the area of a square.

First of all, we know that the sides of a square are all the same length. This makes things really easy.

As with a lot of shape work, there is a formula that you need to learn. So here goes: Area of a square =base x height

Yes, really that is all there is to it.

Find the area of this square Hang on, I only have the length of one side.

Of course, squares sides are all the same.

Area = base x height

Area = 62 x 62 = 3844 mm² As we are working with area units are always squared. e.g cm² m²

There will be no stopping you now! Find the area of this square. Side 3 cm

6 cm²

9 cm²

12 cm²

14 cm²

Can you match the following areas with the squares below?

## Column B

Square side 4 cm
64 cm²
Square side 6 cm
36 cm²
Square side 8cm
16 cm²
Square side 5 cm
64 mm²
Square side 8 mm
25 cm²
Square side 6 m
36 m² Police have cordoned off a square crime scene measuring 2.7m along one wall.  What is the area of the crime scene?

## Column B

Square side 4 cm
64 cm²
Square side 6 cm
36 cm²
Square side 8cm
16 cm²
Square side 5 cm
64 mm²
Square side 8 mm
25 cm²
Square side 6 m
36 m² ## Column B

Square side 4 cm
64 cm²
Square side 6 cm
36 cm²
Square side 8cm
16 cm²
Square side 5 cm
64 mm²
Square side 8 mm
25 cm²
Square side 6 m
36 m² A square dance floor has a side of 8m.  Calculate its area.

## Column B

Square side 4 cm
64 cm²
Square side 6 cm
36 cm²
Square side 8cm
16 cm²
Square side 5 cm
64 mm²
Square side 8 mm
25 cm²
Square side 6 m
36 m² 32 quilted squares are sewn together to make a cover for a bed.  Each square has a side 4 cm.  What is the total area of the cover?

32 cm²

256 cm²

64 cm²

512 cm² The floor of this classroom has side 9m.

 81 m² 18 m² 36 m² 18 tiles 324 tiles 162 tiles What is the floor area? Tiles are laid of size 0.5m. How many tiles are needed to fill the area of the floor?

What is the difference between the area of a square side 5 cm and the area of a square side 35 mm?

12.75 cm²

1275 mm²

21.50 cm²

21500 mm² A square lawn has a side 6m.  The border is 2m wide all the way around the lawn.

 36 m ² 64 m² 100 m² 28 m² 100 m² 75 cm² Calculate the area of the total garden Calculate the area of the border The area of this square is 49 cm².  What is the length of its side?

 36 m ² 64 m² 100 m² 28 m² 100 m² 75 cm² Calculate the area of the total garden Calculate the area of the border
• Question 1 Find the area of this square. Side 3 cm

9 cm²
EDDIE SAYS
Did you apply the formula? Base x height When working with area of a square, you are only usually given one side length. But this is no problem because we know that the sides of the square are all the same length. 3 x 3 = 9 cm²
• Question 2

Can you match the following areas with the squares below?

## Column B

Square side 4 cm
16 cm²
Square side 6 cm
36 cm²
Square side 8cm
64 cm²
Square side 5 cm
25 cm²
Square side 8 mm
64 mm²
Square side 6 m
36 m²
EDDIE SAYS
Applying the formula is now getting easy! Did you spot that some of the units were different? Watch out for this. 8xcm x 8 cm = 64 cm² is a larger area than 8mm x 8mm. Imagine if you had made a mistake when calculating the area of a carpet to lay for Lord Sugar..... You're fired!
• Question 3 Police have cordoned off a square crime scene measuring 2.7m along one wall.  What is the area of the crime scene?

EDDIE SAYS
Often area questions are in the written form. The clues are always in the question. A square crime scene was mentioned with the length of one side of the room. Just apply the formula 2.7 x 2.7 = 7.29 m² That robber does look shifty...
• Question 4 EDDIE SAYS
You will have noticed in this type of question there is no mention of area. This is where your thinking skills are required. To ice the cake across the top it is clearly the area required. 7 x 7 = 49 cm² Likewise with the toast 3.5 x 3.5 = 12.25 cm² That toast looks nice, think I will poach an egg to put on top. Egg on toast, what is not to like?
• Question 5 A square dance floor has a side of 8m.  Calculate its area.

EDDIE SAYS
Just another example of finding area from a written question. 8 x 8 = 64 m² He looks like he can throw some good shapes!
• Question 6 32 quilted squares are sewn together to make a cover for a bed.  Each square has a side 4 cm.  What is the total area of the cover?

512 cm²
EDDIE SAYS
This is just a 2 step question. You have all the knowledge that you need. Area of 1 square = 4 x 4 = 16 cm² Just multiply by 32 16 x 32 = 512 cm² You can do these in your sleep now.
• Question 7 The floor of this classroom has side 9m.

 81 m² 18 m² 36 m² 18 tiles 324 tiles 162 tiles What is the floor area? Tiles are laid of size 0.5m. How many tiles are needed to fill the area of the floor?
EDDIE SAYS
This is a problem that carpet fitters and tilers face all the time. The first part is second nature to you now. 9 x 9 = 81 m² The next part takes a little more thought. You know that one side of the floor measures 9m. To find out how many tiles fit along one side of the wall just divide 9 by 0.5. 9 ÷ 0.5 = 18 18 tiles go along one wall so 18 must also go along the other wall. 18 x 18 = 324 Hey presto job done!
• Question 8

What is the difference between the area of a square side 5 cm and the area of a square side 35 mm?

12.75 cm²
1275 mm²
EDDIE SAYS
Did you spot the difference in units. Very important in this type of question. You could convert either way. 35mm = 3.5 cm 5cm x 5 cm = 25 cm² 3.5 x 3.5 =12.15 cm² 25 - 12.25 = 12.75 cm² or 5cm = 50mm 50 x 50 =2500 35 x 35 = 1225 2500 - 1255 = 1275mm ²
• Question 9 A square lawn has a side 6m.  The border is 2m wide all the way around the lawn.

 36 m ² 64 m² 100 m² 28 m² 100 m² 75 cm² Calculate the area of the total garden Calculate the area of the border
EDDIE SAYS
This is useful if you only want to find out areas of part of a whole square. What do we know? The whole garden including the border has a side of 8m 8 x 8 = 64 m² The lawn is 6 x 6 = 36 m² To find the border just subtract the area of the lawn from the area of the whole garden. 64 - 36 = 28 m² The grass isn't going to grow under your feet, is it?
• Question 10 The area of this square is 49 cm².  What is the length of its side?

EDDIE SAYS
Sometimes we are asked to find side lengths. You know area = base x height = cm² Do the opposite. The opposite of the square is a square root. √49 = 7 cm This time it is not squared units as you only want the side length.
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