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9.01 Review: Perimeter and area

Lesson

Perimeter

Perimeter is all about the distance around the outside, a little like walking around the outside of the school grounds. The perimeter of a polygon (a 2D shape with straight edges) is the total distance around the outside. We can calculate the perimeter of any polygon, no matter how many sides it has by adding up all of the lengths of the sides. 

 

Using formulas

As mathematicians, we want to be as efficient as possible, so we often will use formulas to save time when looking at our basic shapes. Below are some of the key formulas:

Shape Formula

Rectangle

$P=2l+2w$P=2l+2w

 

Square

$P=4l$P=4l

 

 

Practice questions

Question 1

Find the perimeter of the shape given.

Question 2

Find the perimeter of the square shown.

Question 3

A rectangle has a perimeter of $22$22 cm. If its length is $8$8 cm, what is its width?

 

Area

Area is the number of square units needed to cover a surface or figure. For many of our basic shapes, we can use formulas to help make things more efficient. For composite shapes which are made up of many different shapes, we will need to add or subtract the areas of the basic shapes which make it.

Basic shapes

Below is a list of shapes that you should be familiar with and their area formulas.

Shape Area formula

Rectangle

$A=lw$A=lw

 

Square

$A=l^2$A=l2

 

Triangle

$A=\frac{bh}{2}$A=bh2

or

$A=\frac{1}{2}bh$A=12bh

Parallelogram

$A=bh$A=bh

 

Trapezoid

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

 

 

Worked examples

Question 4

Find: The area of this parallelogram

Think: Identify the values for the base and height

Do:

A $=$= $b\times h$b×h
  $=$= $32\times14$32×14 mm2
  $=$= $30\times14+2\times14$30×14+2×14 mm2
  $=$= $420+28$420+28 mm2
  $=$= $448$448 mm2

 

Question 5

Question: A new chocolate bar is to be made with the following dimensions,  the graphic artist needs to know the area of the trapezoid to begin working on a wrapping design.  Find the area.  

Think: I need to identify the base1, base2 and height.  I can see these on the diagram that is given.

Do:

$\text{Area of a Trapezoid}$Area of a Trapezoid  $=$=  $\frac{1}{2}\times\left(\text{Base 1 }+\text{Base 2}\right)\times\text{Height }$12×(Base 1 +Base 2)×Height
  $=$= $\frac{1}{2}\times\left(a+b\right)\times h$12×(a+b)×h
  $=$= $\frac{1}{2}\times\left(4+8\right)\times3$12×(4+8)×3
  $=$= $\frac{1}{2}\times12\times3$12×12×3
  $=$= $18$18 cm2

So now we can find the areas of rectangles, squares, triangles (which are half of a rectangle), parallelograms (like a rectangle), and trapezoids (like half a rectangle).

 

Units

We use special units to describe area, based on the notion of square units described above.  Because the units for length include millimeters, centimeters, meters and kilometers we end up with the following units for area.

square millimeters  = mm2
(picture a square with side lengths of $1$1 mm each - pretty small this one!)

square centimeters = cm2
(picture a square with side lengths of $1$1 cm each - about the size of a fingernail)

square meters = m2
(picture a square with side lengths of $1$1 m each - what do you know that is about this big?)

square kilometers = km2
(picture a square with a side length of $1$1km - I wonder how many of these your town or city is?)

 

Practice questions

Question 6

Find the area of the rectangle shown.

Question 7

Find the area of the triangle shown.

Question 8

Find the area of the parallelogram shown.

Question 9

Find the area of the figure shown.

 

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