Measurement
Perimeter and Area of 2D Shapes
Year 3 · Year 4 · Year 5 · Year 6
- ✓Calculate the perimeter of rectangles and compound shapes.
- ✓Calculate the area of rectangles.
- ✓Calculate the area of compound shapes made from rectangles.
- ✓Calculate the area of triangles.
- ✓Calculate the area of parallelograms.
Key concepts
The perimeter of a 2D shape is the total distance around its outside edge. Imagine walking along all the sides of a shape; the total distance you walk is its perimeter. It is measured in units of length, such as centimetres (cm) or metres (m).
The area of a 2D shape is the amount of surface it covers, or the space inside the shape. Area is measured in square units, such as square centimetres (cm²) or square metres (m²).
To find the area of a rectangle, you multiply its length by its width (or height).
To find the area of a triangle, you multiply its base by its perpendicular height and then divide by 2 (or multiply by ½). The perpendicular height is the straight distance from the base to the opposite vertex, measured at a right angle to the base.
To find the area of a parallelogram, you multiply its base by its perpendicular height. The perpendicular height is the straight distance between the base and the opposite side, measured at a right angle to the base.
Compound shapes are shapes made up of two or more simpler shapes, such as rectangles, triangles, or parallelograms, joined together. To find the perimeter, you add up all the outer edges. To find the area, you can split the compound shape into simpler shapes, calculate the area of each part, and then add them together, or subtract a 'cut-out' area from a larger shape.
Key facts to remember
- 1Perimeter is the distance around the outside of a shape.
- 2Area is the amount of surface a shape covers.
- 3Perimeter is measured in units of length (e.g., cm, m).
- 4Area is measured in square units (e.g., cm², m²).
- 5Area of a rectangle = length × width.
- 6Area of a triangle = ½ × base × height.
- 7Area of a parallelogram = base × height.
- 8Compound shapes can be split into simpler shapes to find their total area.
Worked examples
Example 1
A rectangular garden is 8 metres long and 5 metres wide. Calculate its perimeter and area.
Answer
Perimeter = 26 m, Area = 40 m²
Example 2
Calculate the area of the triangle with a base of 10 cm and a perpendicular height of 6 cm.
Answer
30 cm²
Remember to use the perpendicular height, not the slanted side.
Example 3
A compound shape has an overall length of 12 cm and an overall height of 9 cm. A rectangular section, 5 cm long and 4 cm high, is cut out from one corner. Calculate the area of the remaining shape.
Answer
88 cm²
You can also solve this by splitting the L-shape into two smaller rectangles and adding their areas.
Example 4
A parallelogram has a base of 7 metres and a perpendicular height of 4 metres. Calculate its area.
Answer
28 m²
Make sure to use the perpendicular height, not the slanted side.
Common mistakes
- ✗Confusing perimeter and area, or using the wrong units for each (e.g., cm for area).
- ✗Forgetting to include all sides when calculating the perimeter of a compound shape.
- ✗Using the slanted side of a triangle or parallelogram instead of the perpendicular height when calculating area.
- ✗Forgetting to divide by 2 when calculating the area of a triangle.
- ✗Incorrectly splitting compound shapes or missing parts when calculating their area.
Exam tips
- ★Always draw a diagram or sketch the shape if one isn't provided.
- ★Write down the correct formula before you start calculating.
- ★Pay close attention to the units given in the question and make sure your answer uses the correct units.
- ★For compound shapes, break them down into simpler rectangles, triangles, or parallelograms.
- ★Double-check your calculations, especially for multi-step problems.
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