Lesson 2 of 8 · Grades 3 to 6
Area by counting squares
Area is the amount of surface a shape covers. The first way to measure area is to cover the shape with unit squares and count them.
What area means
Area is the amount of flat surface a shape covers. Length measures one edge; area measures the whole inside. A rug has an area, a wall has an area, and a page has an area. To measure area, we count equal squares, called unit squares.
A unit square is one unit long and one unit wide. If the units are centimetres, each square is 1 cm². The rectangle below is covered by unit squares. Count them and you have the area: 15 square units.
Counting in rows
Counting one square at a time works, but it is slow and easy to muddle. Look for rows instead. The rectangle above has 3 rows with 5 squares in each row. Skip count in fives: 5, 10, 15. Rows turn counting into multiplying, and that idea becomes the rule for rectangles in the next lesson.
When a shape is not a rectangle, count the whole squares first, then deal with the pieces. Tick each square as you count it so you never count one twice.
Whole squares and half squares
A diagonal edge cuts some squares in half. Two half squares make one whole square, so you can pair them up and carry the total forward. The pentagon below sits on a grid of unit squares. It covers 13 whole squares and 2 half squares, which make 1 more square, for an area of 14 square units.
Square units
Area always uses square units, and the unit comes from the grid. A grid of centimetre squares gives square centimetres, written cm². A grid of metre squares gives square metres, written m². The little 2 means the shape was measured in two directions, length and width, not that the number is doubled.
Choose a unit that fits the object. A stamp is measured in square centimetres, a bedroom floor in square metres, and a country in square kilometres. If the unit is too big, the number becomes a tiny fraction, which tells you nothing useful.
Worked example
A path is drawn on a grid of square metres. It covers 12 whole squares and 8 half squares. What is its area?
Step 1: count the whole squares first. There are 12 of them.
Step 2: pair the half squares. Every 2 half squares make 1 whole square, and 8 ÷ 2 = 4 whole squares.
Step 3: add the whole squares and the paired halves. 12 + 4 = 16.
Step 4: label the unit. Each square is 1 m², so the path covers 16 m².
Answer: 16 m².
Counting tip
Mark each square as you count it, or count whole rows at once. When you meet half squares, gather them in pairs first. One pair equals one whole square, so an odd half left over tells you that you have missed its partner somewhere.
Remember
- Area is the flat surface inside a shape.
- Cover the shape with unit squares and count them.
- Count whole squares first, then pair the half squares.
- Write area in square units, such as cm² or m².
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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A rectangle covers 4 rows of 6 unit squares. How many unit squares is that?
Show answer
24 unit squares. 4 × 6 = 24.
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A square covers 5 rows of 5 unit squares. What is its area?
Show answer
25 square units. 5 × 5 = 25.
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A shape covers 7 whole squares and 4 half squares. What is its area?
Show answer
9 square units. Four half squares make 2 whole squares, and 7 + 2 = 9.
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Which unit fits the area of a postage stamp: square centimetres or square metres?
Show answer
Square centimetres. A stamp is only a few centimetres wide, so square metres are far too big.
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A shape covers 30 unit squares and each square is 1 cm². What is its area?
Show answer
30 cm². Count the squares: 30 square centimetres.
Puzzle · Grid count
Puzzle time
This shape is drawn on a grid of unit squares. It covers whole squares only. How many square units is its area?
Show a hint
Count the shaded squares row by row: 1, then 3, then 5, then 3, then 1.
Show the answer
Answer: 13. Row by row the shape covers 1 + 3 + 5 + 3 + 1 = 13 square units.