Area and Perimeter — NSW Year 8 Maths
The distance around a shape and the space it covers, from fencing a paddock to a slice of pizza. Twelve subtopics and 240 practice questions, each with a fully worked solution, aligned to NESA outcomes MA4-LEN-C-01 and MA4-ARE-C-01.
Area and Perimeter in NSW Year 8
Perimeter is the distance around the edge of a shape and area is the flat surface it covers. Year 7 dealt with straight-sided shapes such as rectangles, triangles and parallelograms. In Year 8, students add the trapezium, kite and rhombus, tackle harder composite shapes and work with circles for the first time: the parts of a circle, the number \(\pi\), circumference, arc length and the areas of circles and sectors.
The twelve subtopics below begin with perimeter and metric units of area, then work through the area formula for each type of quadrilateral and for composite shapes. The second half turns to circles, moving from naming the parts to circumference, arcs and the perimeter of sectors, then the areas of circles and sectors. Area and Perimeter is one of the 14 topics in NSW Year 8 Maths and belongs to the Measurement and Space strand (NESA outcomes MA4‑LEN‑C‑01 and MA4‑ARE‑C‑01). Circle areas feed straight into cylinders in the next topic, Volume, and into surface area in Stage 5.
Subtopics
Area and Perimeter: common questions
What do you learn in Area and Perimeter in Year 8?
You find the perimeter and area of triangles, parallelograms, trapeziums, kites, rhombuses and composite shapes, convert between units such as \(\text{m}^2\) and hectares, and work with circles: circumference, arc length and the areas of circles and sectors.
What is the area formula for a trapezium?
Add the two parallel sides, halve the total and multiply by the perpendicular height: \(A = \frac{1}{2}(a + b)h\). Parallel sides of 6 cm and 10 cm that are 4 cm apart give \(A = \frac{1}{2} \times 16 \times 4 = 32\text{ cm}^2\).
How do you find the circumference and area of a circle?
Use \(C = \pi d\) or \(C = 2\pi r\) for the distance around, and \(A = \pi r^2\) for the area. A circle with a radius of 5 cm has \(C = 10\pi \approx 31.4\text{ cm}\) and \(A = 25\pi \approx 78.5\text{ cm}^2\).
Which NESA outcomes cover area and perimeter in Year 8?
Area and Perimeter sits in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcomes MA4‑LEN‑C‑01 (perimeter, circumference and arc length) and MA4‑ARE‑C‑01 (area, including circles and sectors).
What comes after area and perimeter in Year 8?
The area of a cross-section is the first step in every volume question, so the next topic, Volume, uses these formulas for prisms and cylinders. In Stage 5 they are used again to find the surface area of prisms and cylinders.