Area

measurementandspace core

Area | NSW Curriculum Website

• 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 - area of rectangles	- converting units of area - 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 - 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 - features of circles, $\pi$	- converting units of area - 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 $1{\text{cm}}^2=100{\text{mm}}^2$, $1{\text{m}}^2=10000{\text{cm}}^2$, $1\text{ha}=10000{\text{m}}^2$, and $1{\text{km}}^2=1000000{\text{m}}^2=100\text{ha}$