#MeasurementAndSpace #Core >[!info]- [Area | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-4/fa3b012530) >- MA4-ARE-C-01 applies knowledge of area and composite area involving triangles, quadrilaterals and circles to solve problems ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | --------------------------------------- | ------------------------------------------------------------------- | --------------------------------------------------------------------- | | [[Two-dimensional Spatial Structure A]] | - units of area<br>- area of rectangles | - converting units of area<br>- problems involving area of rectangles | | [[Two-dimensional Spatial Structure B]] | - finding area by subdivision; area of a parallelogram and triangle | - deriving area formulas. | | [[Fractions Decimals Percentages]] | - fraction of a quantity<br>- rounding decimals | - calculating area of a sector | | [[Algebraic Techniques]] | -generalising relationships | - deriving area formulas | | [[Indices]] | - squaring and square roots | - area calculations | | [[Equations]] | - using formulas | - solving problems involving area formulas | | [[Length]] | - converting units of length<br>- features of circles, $\pi$ | - converting units of area<br>- area of a circle | | [[Right-angled Triangles]] | - Pythagoras' theorem | - Finding diagonals or side lengths of quadrilaterals | | [[Properties of Geometrical Figures]] | - properties of the special quadrilaterals | - calculating area of special quadrilaterals | ## [[Develop and use formulas to find the area of rectangles, triangles and parallelograms to solve problems.pdf]] - Apply the formula to find the area of a rectangle or square: $A=lb$, where $l$ is the length and $b$ is the breadth (or width) of the rectangle or square - Develop and apply the formula to find the area of a triangle: $A=\frac{1}{2}bℎ$, where $b$ is the base length and ℎ is the perpendicular height - Develop and apply the formula to find the area of a parallelogram: $A=bh$ where $b$ is the base length and ℎ is the perpendicular height - Calculate the area of composite figures that can be dissected into rectangles, squares, parallelograms or triangles to solve problems ## [[Develop and use the formula to find the area of circles and sectors to solve problems.pdf]] - Develop and apply the formula to find the area of a circle: $A=\pi r^2$, where $r$ is the length of the radius - Explain how the area of a sector can be developed from the area of a circle $A=\frac{\theta}{360}\times \pi r^2$ - Find the area of quadrants, semicircles and sectors, and apply these formulas in the context of real-life problems - Calculate the areas of composite shapes involving quadrants, semicircles and sectors to solve problems ## [[Develop and use the formulas to find the area of trapeziums, rhombuses and kites to solve problems.pdf]] - Develop and apply the formula to find the area of a kite or rhombus: $A=\frac{1}{2}xy$, where $x$ and $y$ are the lengths of the diagonals - Develop and apply the formula to find the area of a trapezium: $A=\frac{h}{2} (a+b)$, where ℎ is the perpendicular height and $a$ and $b$ are the lengths of parallel sides - Calculate the area of composite shapes involving trapeziums, kites and rhombuses to solve problems ## [[Choose appropriate units of measurement for area and convert between units.pdf]] - Choose an appropriate unit to measure the area of different shapes and surfaces, and justify the choice - Convert between metric units of area using $1\ \text{cm}^2\ =100\ \text{mm}^2$, $1\ \text{m}^2\ =10\ 000\ \text{cm}^2$, $1\ \text{ha}\ =10\ 000\ \text{m}^2$, and $1\ \text{km}^2\ =1\ 000\ 000\ \text{m}^2=100\ \text{ha}$