Year 5: Area of rectangles, squares and irregular shapes
Part of the Year 5 units, perimeter, area, volume and time chapter. Chapter overview · whole chapter on one page
Area of rectangles, squares and irregular shapes
The area is the amount of surface inside a shape. We measure it by counting squares. A square with sides of 1 cm has an area of 1 square centimetre, written cm². A square with sides of 1 m has an area of 1 square metre, written m².
For a rectangle, we do not need to count every square. The picture below has 7 squares in each row and 5 rows. 5 rows of 7 squares is 35 squares, so the area is 35 cm². That is the same as length × width.
Key ideas
- Area of a rectangle or square = length × width.
- Area is measured in square units: cm² or m². Area is not measured in cm or m.
- For an irregular shape, count the whole squares. Two part squares together make one whole square.
- A square is a rectangle where all four sides are equal, so its area is side × side.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.7 × 5 = 35
- Write the answer with square units. We are counting squares, so the unit is squared.35 cm²
Check. 5 × 7 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.9 × 9 = 81
- Write the answer with square units. We are counting squares, so the unit is squared.81 cm²
Check. 9 × 9 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Count the whole squares, then count the part squares and make pairs. Each pair is one whole square.
- Count the whole squares inside the shape. A whole square is completely inside the outline.20 whole squares
- Count the part squares, then pair them up. Each part square is exactly half a square. Two of them make one whole square.4 part squares ÷ 2 = 2 whole squares
- Add the two counts. The total is the area of the shape in squares.20 + 2 = 22
- Write the answer with square units. This is an estimate, so we say about.about 22 cm²
Check. Count the shape again, row by row, to check you have not missed a square. ✓
Watch out. Do not count a part square as a whole square, and do not leave out the part squares.
Watch out
Area is not the same as perimeter. The perimeter is a length (cm) and the area is a number of squares (cm²). Also, 1 m² is not 100 cm². A square metre is 100 cm by 100 cm, which is 10 000 cm².Exercise 8D Area of rectangles and squares
Non-calculatorKey words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.5 × 4 = 20
- Write the answer with square units. We are counting squares, so the unit is squared.20 cm²
Check. 4 × 5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.9 × 6 = 54
- Write the answer with square units. We are counting squares, so the unit is squared.54 cm²
Check. 6 × 9 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.12 × 3 = 36
- Write the answer with square units. We are counting squares, so the unit is squared.36 cm²
Check. 3 × 12 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.6 × 10 = 60
- Write the answer with square units. We are counting squares, so the unit is squared.60 cm²
Check. 10 × 6 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.6 × 6 = 36
- Write the answer with square units. We are counting squares, so the unit is squared.36 cm²
Check. 6 × 6 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.11 × 11 = 121
- Write the answer with square units. We are counting squares, so the unit is squared.121 cm²
Check. 11 × 11 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.12 × 12 = 144
- Write the answer with square units. We are counting squares, so the unit is squared.144 cm²
Check. 12 × 12 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.7 × 7 = 49
- Write the answer with square units. We are counting squares, so the unit is squared.49 cm²
Check. 7 × 7 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.2.5 × 4 = 10
- Write the answer with square units. We are counting squares, so the unit is squared.10 m²
Check. 4 × 2.5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.1.5 × 2 = 3
- Write the answer with square units. We are counting squares, so the unit is squared.3 m²
Check. 2 × 1.5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.3.2 × 2.5 = 8
- Write the answer with square units. We are counting squares, so the unit is squared.8 m²
Check. 2.5 × 3.2 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.0.5 × 6 = 3
- Write the answer with square units. We are counting squares, so the unit is squared.3 m²
Check. 6 × 0.5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Find the area of each shape, then compare the two numbers.
- Find the area of the rectangle. Multiply the length by the width.3 × 8 = 24 cm²
- Find the area of the square. Multiply the side by itself.5 × 5 = 25 cm²
- Compare. The bigger number is the bigger area.25 > 24
- Write the answer. The square has the bigger area, 25 cm² compared with 24 cm².
Check. The square has area 25 cm², which is 1 square more. ✓
Watch out. The square looks like the rectangle in size, but its area is bigger.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Area = length × width. Use the area and one side to find the other side.
- Write the rule. The area is the length times the width.area = length × width
- Divide the area by the known width. The missing length is the area divided by the width.48 ÷ 6 = 8
- Write the answer. 8 cm
Check. 8 × 6 = 48 cm². ✓
Watch out. Divide the area by the side you know. Do not subtract the width from the area.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Count the whole squares, then count the part squares and make pairs. Each pair is one whole square.
- Count the whole squares inside the shape. A whole square is completely inside the outline.14 whole squares
- Count the part squares, then pair them up. Each part square is exactly half a square. Two of them make one whole square.4 part squares ÷ 2 = 2 whole squares
- Add the two counts. The total is the area of the shape in squares.14 + 2 = 16
- Write the answer with square units. This is an estimate, so we say about.about 16 cm²
Check. Count the shape again, row by row, to check you have not missed a square. ✓
Watch out. Do not count a part square as a whole square, and do not leave out the part squares.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Count the whole squares, then count the part squares and make pairs. Each pair is one whole square.
- Count the whole squares inside the shape. A whole square is completely inside the outline.21 whole squares
- Count the part squares, then pair them up. Each part square is exactly half a square. Two of them make one whole square.6 part squares ÷ 2 = 3 whole squares
- Add the two counts. The total is the area of the shape in squares.21 + 3 = 24
- Write the answer with square units. This is an estimate, so we say about.about 24 cm²
Check. Count the shape again, row by row, to check you have not missed a square. ✓
Watch out. Do not count a part square as a whole square, and do not leave out the part squares.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Count the squares in each row and the number of rows, then multiply.
- Count the squares in one row. Each row has the same number of squares.6 squares in each row
- Count the rows. Count the rows from top to bottom.3 rows
- Multiply. The total number of squares is the area.6 × 3 = 18
- Write the answer. 18 cm²
Check. Count every square one by one: 18 squares. ✓
Watch out. Write the unit as cm², because you are counting squares.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.4.5 × 3 = 13.5
- Write the answer with square units. We are counting squares, so the unit is squared.13.5 m²
Check. 3 × 4.5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.40 × 30 = 1,200
- Write the answer with square units. We are counting squares, so the unit is squared.1,200 cm²
Check. 30 × 40 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Find the area of each rectangle, then the perimeter of each.
- Find the areas. Multiply the length by the width.10 × 2 = 20 cm², and 5 × 4 = 20 cm². The areas are the same.
- Find the perimeters. Add all four sides of each rectangle.10 + 2 + 10 + 2 = 24 cm, and 5 + 4 + 5 + 4 = 18 cm.
- Write the answer. The areas are the same, but the perimeters are not.Same area: yes. Same perimeter: no.
Check. Two shapes can have the same area and different perimeters. ✓
Watch out. Area and perimeter measure different things. Do not expect one to match the other.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. List the pairs of whole-number sides that multiply to make 36, then find the perimeter of each.
- List the pairs. Each pair of sides must multiply to make 36.1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
- Find the perimeter of each pair. Perimeter = 2 × (length + width).2 × 37 = 74, 2 × 20 = 40, 2 × 15 = 30, 2 × 13 = 26, 2 × 12 = 24
- Find the smallest perimeter. The pair that is closest to a square has the smallest perimeter.24 is the smallest.
- Write the answer. 6 cm by 6 cm, with a perimeter of 24 cm.
Check. 6 × 6 = 36. A square has the smallest perimeter for a given area. ✓
Watch out. Check each pair. Do not stop at the first pair you find.