Measurement

Ontario 09 Applied (MFM1P)

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`

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

Solve problems involving the areas and perimeters of composite two-dimensional shapes (i.e., combinations of rectangles, triangles, parallelograms, trapezoids, and circles)