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	Prerequisite relationships
Multiplicative Relations A	- Find the product of numbers → Calculate the area of a rectangle
Multiplicative Relations B	- Multiply and divide decimals by powers of 10 → Convert between units of area
Two-dimensional Spatial Structure A	- Calculate the area of a rectangle (revisited content)
Two-dimensional Spatial Structure B	- Find the area of composite figures (revisited content) - Identify the base and perpendicular height → Find the area of a parallelogram - Find the area of a parallelogram (revisited content) - Find the area of a triangle (revisited content)
Algebraic Techniques	- Substitute values into algebraic expressions → Find the area of a circle
Indices	- Evaluate numbers in index notation → Find the area of a circle
Equations	- Solve 2-step linear equations → Find an unknown given a trapezium area - Solve 2-step linear equations → Find an unknown side given the area - Solve quadratic equations of the form $a{x}^2=c$ → Find an unknown given a circle or sector area
Length	- Identify the features of circles → Halve the diameter to find the radius - Define $\pi$ → Find the area of a circle
Right-angled Triangles	- Find a side using Pythagoras’ theorem → Find areas requiring Pythagoras’ theorem

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 $1{\text{km}}^2=1000000{\text{m}}^2=100\text{ha}$