Section A — Chapters 1–22
Applied Measure I
Junior Cycle — 1st Year
- ✓By the end of this lesson students will be able to identify and use standard units of length, area, and volume.
- ✓By the end of this lesson students will be able to calculate the perimeter and area of squares and rectangles.
- ✓By the end of this lesson students will be able to recognise and draw nets of rectangular solids (cuboids and cubes).
- ✓By the end of this lesson students will be able to calculate the surface area of rectangular solids.
Key concepts
Length is a measure of distance. Standard units include millimetres (mm), centimetres (cm), metres (m), and kilometres (km). It is important to know how to convert between these units: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.
The perimeter of a 2D shape is the total distance around its boundary. It is measured in units of length (e.g., cm, m).
The area of a 2D shape is the amount of surface it covers. It is measured in square units (e.g., cm², m²).
A net is a 2D shape that can be folded to form a 3D solid. It shows all the faces of the solid laid out flat.
A 3D shape with six rectangular faces. Opposite faces are identical. It has length, width, and height.
A special type of rectangular solid where all six faces are identical squares. All edges are of equal length.
The surface area of a 3D solid is the total area of all its faces. It is measured in square units (e.g., cm², m²). To find the surface area, you calculate the area of each face and add them together, often by using the net of the solid.
Key facts to remember
- 11 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.
- 2Perimeter is the distance around a 2D shape, measured in units of length (e.g., cm, m).
- 3Area is the amount of surface a 2D shape covers, measured in square units (e.g., cm², m²).
- 4Perimeter of a rectangle = 2(length + width). Area of a rectangle = length × width.
- 5Perimeter of a square = 4 × side. Area of a square = side².
- 6A net is a 2D shape that can be folded to make a 3D solid.
- 7Surface area is the total area of all the faces of a 3D solid, measured in square units.
- 8A cuboid has 6 rectangular faces, a cube has 6 square faces.
Worked examples
Example 1
A rectangular garden has a length of 12 metres and a width of 750 centimetres. Calculate its perimeter and area. Give your answers in metres and square metres respectively.
Answer
Perimeter = 39 m, Area = 90 m².
Always ensure all dimensions are in the same units before calculating perimeter or area.
Example 2
A rectangular solid has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Calculate its surface area.
Answer
Surface Area = 62 cm².
Imagine unfolding the solid into a net to visualise all six faces.
Example 3
A cube has an edge length of 4 cm. Calculate its surface area.
Answer
Surface Area = 96 cm².
For a cube, all faces are squares of the same size, simplifying the calculation.
Common mistakes
- ✗Using length units (e.g., cm) for area calculations instead of square units (e.g., cm²).
- ✗Forgetting to convert all dimensions to the same unit before performing calculations.
- ✗Confusing the formulas for perimeter and area.
- ✗Missing one or more faces when calculating the surface area of a 3D solid from its net.
- ✗Incorrectly multiplying or adding dimensions when calculating surface area (e.g., only calculating the area of three unique faces for a cuboid and not multiplying by 2).
Exam tips
- ★Always draw a clear diagram of the shape, labelling all given dimensions.
- ★Write down the correct formula before substituting values into it.
- ★Double-check that all units are consistent before you start calculating. If they are not, convert them first.
- ★Show all your working steps clearly, as marks are often awarded for method even if the final answer is incorrect.
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