Length

Length | NSW Curriculum Website

MA4-LEN-C-01 applies knowledge of the perimeter of plane shapes and the circumference of circles to solve problems

📖 Prior Knowledge

Content	Prior knowledge	Used for
Geometric Measure A	- converting units of length - measuring lengths for perimeter	- perimeter calculations
Fractions Decimals Percentages	- irrational numbers - fraction of a quantity - rounding decimals	- $π$ - calculating arc length
Algebraic Techniques	- generalising relationships	- establishing circumference formula
Equations	- using formulas	- calculating circumference and arc length

Solve problems involving the perimeter of plane shapes, including parallelograms, trapeziums, rhombuses and kites
Solve problems relating to the perimeter of simple composite figures
Compare methods of solution for finding perimeter and evaluate the efficiency of those methods

Identify and describe the relationship between circle features, including the radius, diameter, arc, chord, sector and segment of a circle, and a tangent to a circle
Define $π$ as the ratio of the circumference to the diameter of any circle
Verify that the number $π$ is a constant and develop the formula for the circumference of a circle
Apply the formula for the circumference of a circle in terms of the diameter $d$ or radius $r$ (circumference of a circle $= π d$ or $= 2 π r$ ) to solve related problems to solve related problems
Establish the arc length formula $l = \frac{θ}{360} \times 2 π r$ where $l$ is the arc length and $θ$ is the angle subtended at the centre by the arc
Solve problems by finding arc lengths and the perimeter of sectors, giving an exact answer in terms of $π$ or an approximate answer
Find the perimeter of quadrants, semicircles and simple composite figures consisting of 2 shapes in a variety of contexts, including using digital tools