Measurement

NZ Level 5

Area Composite Shapes

Lesson

We have already had a look at combining 2D shapes together and finding the area of composite shapes. But since then we have learnt about the areas of a whole lot more shapes.

Let's just look at a summary of areas of 2D shapes we have looked at so far with our shape robot:

The key skills you need to remember when thinking about composite shapes are to consider

- can the shape be considered as a larger easier shape with smaller bits missing
- can the shape be considered the sum of a number of smaller shapes

$\text{Area of a Rectangle }=\text{length }\times\text{width }$Area of a Rectangle =length ×width

$A=L\times W$`A`=`L`×`W`

$\text{Area of a Square }=\text{Side }\times\text{Side }$Area of a Square =Side ×Side

$A=S\times S$`A`=`S`×`S`

$\text{area of a triangle }=\frac{1}{2}\times\text{base }\times\text{height }$area of a triangle =12×base ×height

$A=\frac{1}{2}bh$`A`=12`b``h`

$\text{Area of a Parallelogram }=\text{Base }\times\text{Height }$Area of a Parallelogram =Base ×Height

$A=b\times h$`A`=`b`×`h`

$\text{Area of a Trapezium}=\frac{1}{2}\times\left(\text{Base 1 }+\text{Base 2 }\right)\times\text{Height }$Area of a Trapezium=12×(Base 1 +Base 2 )×Height

$A=\frac{1}{2}\times\left(a+b\right)\times h$`A`=12×(`a`+`b`)×`h`

$\text{Area of a Kite}=\frac{1}{2}\times\text{diagonal 1}\times\text{diagonal 2}$Area of a Kite=12×diagonal 1×diagonal 2

$A=\frac{1}{2}\times x\times y$`A`=12×`x`×`y`

$\text{Area of a Rhombus }=\frac{1}{2}\times\text{diagonal 1}\times\text{diagonal 2}$Area of a Rhombus =12×diagonal 1×diagonal 2

$A=\frac{1}{2}\times x\times y$`A`=12×`x`×`y`

$\text{Area of a circle }$Area of a circle

$A=\pi r^2$`A`=π`r`2

$\text{Area of a sector }$Area of a sector

$A=\frac{\text{angle of sector}}{360}\times\pi r^2$`A`=angle of sector360×π`r`2

Find the total area of the figure shown.

Find the total area of the figure shown.

Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders