Area and perimeter of rectangles
Apply the area formula (l × w) and perimeter formula (2l + 2w) for rectangles including squares in real-world and mathematical problems; calculate and compare areas using standard units (cm², m²) and estimate areas of irregular shapes
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- Find the width of a room given area = 48 m² and length = 8 m
- Calculate the area of a square with side 7.5 cm
- Estimate the area of an irregular pond drawn on a cm² grid
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The area of a rectangle tells you how much flat space it covers. You find it by multiplying the length by the width: area = length × width. Measure in centimetres and you get square centimetres (cm²). Measure in metres and you get square metres (m²). A square is a rectangle with four equal sides, so its area is side × side.
A square tile has sides of 6.5 cm. A square is a rectangle with equal sides, so area = 6.5 × 6.5 = 42.25 cm². The units stay square centimetres, because you are counting squares that are 1 cm across.
A hall has an area of 36 m² and a length of 9 m. Area = length × width, so the width must be 36 ÷ 9 = 4 m. When you know the area and one side, divide to find the other side.
The perimeter is the distance all the way around the outside. Add the length of every side to find it. In a rectangle the opposite sides match, so there is a shortcut: perimeter = 2 × length + 2 × width. Perimeter is measured in plain centimetres or metres, not square units.
Not every shape is a tidy rectangle. To estimate the area of something like a pond, draw it on a grid of squares. Count the whole squares inside it first. Then look at the part-covered squares and guess how much they add up to. Combine the two counts for your estimate.
Area = length × width, perimeter of a rectangle = 2 × length + 2 × width, and for odd shapes, count grid squares to estimate.
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How to Find the Area of Irregular Shapes
Odd shapes still have areas you can estimate. First method: lay the shape on a centimetre grid and count. Full squares count as one each. Pair up half squares into wholes. A pond with 14 full squares and 8 halves is about 14 + 4 = 18 square cm. Second method: split the shape into rectangles you know. Work out each rectangle with length x width, then add the parts. A wobbly pond might split into a 4 by 3 piece and a 2 by 2 piece: 12 + 4 = 16. Both routes give an estimate, not an exact answer, and that is fine for puddles and ponds.
9 Ways to Find Perimeter
Perimeter is the walk round a shape. Add every side and you have it. Rectangles have a shortcut: opposite sides match, so perimeter is 2 x length + 2 x width. A 9 by 6 rectangle gives 18 + 12 = 30 cm. Squares are even quicker: 4 x side. Missing sides work backwards: if a rectangle has perimeter 24 cm and one side 8 cm, the other pair shares 24 - 16 = 8 cm, so each is 4 cm. Keep perimeter and area apart: adding walks the edge, multiplying fills the inside.
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