#MeasurementAndSpace #Core >[!info]- [Length | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-4/fa498c8819) >- 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<br>- measuring lengths for perimeter | - perimeter calculations | | [[Fractions Decimals Percentages]] | - irrational numbers<br>- fraction of a quantity<br>- rounding decimals | - $\pilt;br>- calculating arc length | | [[Algebraic Techniques]] | - generalising relationships | - establishing circumference formula | | [[Equations]] | - using formulas | - calculating circumference and arc length | ## [[Solve problems involving the perimeter of various quadrilaterals and simple composite figures.pdf]] - 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 ## [[Describe the relationships between the features of circles.pdf]] - 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 $\pi$ as the ratio of the circumference to the diameter of any circle - Verify that the number $\pi$ 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 $=\pi d$ or $=2\pi r$) to solve related problems to solve related problems - Establish the arc length formula $l=\frac{\theta}{360}\times 2\pi r$ where $l$ is the arc length and $\theta$ 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 $\pi$ 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