Measures
Perimeter and Area of Rectangles and Irregular Shapes
3rd Class · 4th Class · 5th Class · 6th Class
- ✓By the end of this lesson students will be able to define and calculate the perimeter of a rectangle.
- ✓By the end of this lesson students will be able to define and calculate the area of a rectangle.
- ✓By the end of this lesson students will be able to identify and use appropriate units for perimeter and area.
- ✓By the end of this lesson students will be able to estimate the area of irregular shapes by counting squares on a grid.
Key concepts
The perimeter of a shape is the total distance around its outside edge. Imagine walking around the edge of a field; the distance you walk is the perimeter. We measure perimeter in linear units like centimetres (cm), metres (m), or kilometres (km).
The area of a shape is the amount of surface it covers. Imagine painting a wall; the amount of paint you need depends on the area of the wall. We measure area in square units like square centimetres (cm²), square metres (m²), or square kilometres (km²).
A rectangle has four straight sides, with opposite sides being equal in length. To find the perimeter, you add the lengths of all four sides. If you know the length (L) and the width (W), you can add L + W + L + W, or you can use the formula.
To find the area of a rectangle, you multiply its length by its width. This tells you how many square units fit inside the rectangle.
For shapes that are not regular (like rectangles or squares), we can estimate their area by drawing them on a grid of squares. We count all the full squares inside the shape. Then, we count the partial squares (squares that are partly inside the shape). We usually count partial squares that are more than half-filled as a full square, and ignore those less than half-filled. Sometimes, we count two half-filled squares as one full square.
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 linear units (e.g., cm, m).
- 4Area is measured in square units (e.g., cm², m²).
- 5The perimeter of a rectangle = 2 × (Length + Width).
- 6The area of a rectangle = Length × Width.
- 7To estimate the area of an irregular shape, count full squares and combine partial squares (e.g., two half-squares make one full square).
Worked examples
Example 1
A rectangular garden has a length of 8 metres and a width of 5 metres. Calculate its perimeter and its area.
Answer
The perimeter of the garden is 26 m. The area of the garden is 40 m².
Remember to use the correct units for perimeter (m) and area (m²).
Example 2
A school hall is 15 metres long and 10 metres wide. What is the area of the hall? If a carpet costs €12 per square metre, how much would it cost to carpet the entire hall?
Answer
The area of the hall is 150 m². It would cost €1800 to carpet the entire hall.
This problem combines calculating area with a real-world cost calculation.
Example 3
Estimate the area of the irregular shape drawn on the grid below. Each square on the grid represents 1 cm².
Answer
The estimated area of the irregular shape is 16 cm².
Estimating area of irregular shapes can vary slightly depending on how partial squares are counted. Be consistent with your method.
Common mistakes
- ✗Confusing perimeter and area, for example, calculating area when perimeter is asked for.
- ✗Using the wrong units in the answer (e.g., writing 'cm' for area instead of 'cm²').
- ✗Forgetting to add all four sides when calculating the perimeter of a rectangle, or only adding length and width.
- ✗Incorrectly counting partial squares when estimating the area of irregular shapes.
- ✗Not including any units at all in the final answer.
Exam tips
- ★Always read the question carefully to understand if you need to find the perimeter or the area.
- ★Draw a simple diagram of the shape if one is not provided, and label the sides with the given measurements.
- ★Double-check your calculations, especially when multiplying or adding multiple numbers.
- ★Make sure to write down the correct units (cm, m, cm², m²) with your final answer.
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