Area and Volume — NSW Year 7 Maths
The distance around a shape, the flat space it covers and what a box or tank holds. Twelve subtopics and 240 practice questions, each with a fully worked solution, aligned to NESA outcomes MA4-LEN-C-01, MA4-ARE-C-01 and MA4-VOL-C-01.
Area and Volume in NSW Year 7
Area and Volume is where Year 7 maths meets everyday measuring. Perimeter is the distance around the edge of a shape, area is the amount of flat surface it covers, and volume is the space a solid takes up. In Year 7, students use formulas for rectangles, triangles and parallelograms, break awkward shapes into simpler pieces, find the volume of rectangular prisms and move confidently between units such as \(\text{cm}^2\), hectares, \(\text{cm}^3\) and litres.
The twelve subtopics below start with a refresher on metric units and perimeter, then build up area one shape at a time before combining shapes. The second half moves into three dimensions: cubic units, rectangular and composite prisms, the link between volume and capacity, and the views and cross-sections of solids. Area and Volume is one of the 13 topics in NSW Year 7 Maths and sits in the Measurement and Space strand (NESA outcomes MA4‑LEN‑C‑01, MA4‑ARE‑C‑01 and MA4‑VOL‑C‑01). Later in Stage 4 it extends to circles, trapeziums, kites and cylinders.
Subtopics
Area and Volume: common questions
What do you learn in Area and Volume in Year 7?
You find the perimeter and area of rectangles, triangles, parallelograms and composite shapes, and the volume of rectangular prisms and solids built from them. You also change between metric units for length, area, volume and capacity.
How do you work out the area of a triangle?
Multiply the base by the perpendicular height and halve the result. A triangle with a base of 10 cm and a height of 6 cm has an area of \(\frac{1}{2} \times 10 \times 6 = 30\text{ cm}^2\).
How many cubic centimetres are in a cubic metre?
There are \(1\,000\,000\text{ cm}^3\) in \(1\text{ m}^3\), not 100. A 1 m cube is 100 cm along each edge, so its volume is \(100 \times 100 \times 100 = 1\,000\,000\text{ cm}^3\). Using the length fact (\(1\text{ m} = 100\text{ cm}\)) for cubic units is a common mistake.
Which NESA outcomes cover area and volume?
Area and Volume sits in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcomes MA4‑LEN‑C‑01 (perimeter), MA4‑ARE‑C‑01 (area) and MA4‑VOL‑C‑01 (volume), usually started in Year 7.
What comes after area and volume in Year 7?
Later in Stage 4 students find the circumference and area of circles, the area of trapeziums, kites and rhombuses, and the volume of other prisms and cylinders. In Stage 5 this grows into surface area.