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Measurement, NAP-L4-CA32

Angenie makes native American textiles.

She uses 16 identical leather equilateral triangles to make a headband.

The perimeter of each triangle is 12 centimetres.
 


 

What is the length of the headband?

 
 
 
 
 
32 centimetres 34 centimetres 64 centimetres 96 centimetres 102 centimetres
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`34\ text(centimetres)`

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`text(Perimeter = 12 cm)\ \ =>\ \ text(1 side = 4 cm)`

`text(Length)` `= (8 xx 4)+(0.5 xx 4)`  
  `=34\ text(centimetres)`  

Measurement, NAP-K4-CA38 SA

Leigh is making a stained glass window in the shape of a hexagon.

It uses aluminium bars for the frame and supports.

The supports are parallel with the sides of the frame, as shown below.
 

 
How many metres of aluminium bar are used to make this window?

   metres
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`12\ text(m)`

Show Worked Solution
`text(Outside perimeter)` `= 4 xx 0.8 + 2 xx 0.6`
  `= 3.2 + 1.2`
  `= 4.4\ text(m)`

 
`text{(Note that through parallelogram properties, the top side)`

`text{width is half the width of the horizontal middle length.)}`

 
`text(Length of internal supports)`

`= 2 xx (4 xx 0.8) + 1.2`

`= 6.4 + 1.2`

`= 7.6\ text(m)`

 
`:.\ text(Total length of aluminium bar)`

`= 4.4 + 7.6`

`= 12\ text(m)`

Measurement, NAP-K4-CA10

Adam is laying tiles that are shaped like a parallelogram.
 


 

The longer sides are 2.5 times the length of the shorter sides.

What is the perimeter of one of the tiles?

42 cm 84 cm 96 cm 360 cm
 
 
 
 
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`84\ text(cm)`

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`text(Perimeter)` `= 12 xx 2 + (12 xx 2.5) xx 2`
  `= 24 + 30 xx 2`
  `= 84\ text(cm)`

Measurement, NAP-J4-CA23

Guy is placing door casing on the top and both sides of 2 doors, as pictured below.
 

 
How many metres of door casing does he need?

`text(4.63 m)` `text(6.74 m)` `text(9.26 m)` `text(67.4 m)`
 
 
 
 
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`text(6.74 m)`

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`text(Metres of door casing needed)`

`= (2110 xx 2) + 2520`

`= 6740\ text(mm)`

`= 6.74\ text(m)`

Measurement, NAP-D4-CA27 SA

Poppy draws a quadrilateral with a perimeter of 50 centimetres.

What is the maximum possible area of Poppy's quadrilateral?

   square centimetres
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`156.25\ text(cm²)`

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`text(The maximum area will occur when the)`

`text(quadrilateral is a square.)`

`=>\ text(Length of side) = 50/4 = 12.5\ text(cm)`

 

`:.\ text(Maximum area)` `= 12.5 xx 12.5`
  `= 156.25\ text(cm²)`

Measurement, NAP-F4-NC31 SA

A farmer uses an existing stone wall and fencing to create a large grazing paddock for his sheep, as shown in the diagram below.

The fencing has 3-strand wiring which is also shown below.
 

 
How many kilometres of wire will be required?

  kilometres
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`5.7\ text(km)`

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`text(Fencing required)`

`= 3xx (450 + 200 + 150 + 500 + 600)`

`= 3 xx 1900`

`= 5.7\ text(km)`

Algebra, NAP-F4-NC12

The rhombus below has a side length `d`.
 

 
Which expression cannot be used for the perimeter?

`2 xx (d + d)` `d xx 4` `d xx d` `d + d + 2 xx d`
 
 
 
 
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`d xx d`

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`d xx d`

Measurement, NAP-H4-NC27

A regular hexagon is formed using equilateral triangles.

It has a perimeter of 18 cm, and is cut in half.
 

 

 
What it the perimeter of half of the hexagon?

`text(7 cm)` `text(9 cm)` `text(12 cm)` `text(14 cm)` `text(15 cm)`
 
 
 
 
 
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`text(15 cm)`

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`text(The length of each side of one triangle)`

`=18/12`

`= 1.5\ text(cm)`

`:.\ text(Perimeter of half a hexagon)`

`=3+3+3 + (4 xx 1.5)`

`=15\ text(cm)`

Algebra, NAP-H4-NC31 SA

Renee created a shape using equilateral triangles and squares.

She begins by using a triangle with side length 1 cm.

She then adds a square, then another triangle, then a square etc... until she has 5 triangles and 5 squares.
 
 

 

What will the perimeter of the whole shape be?

   cm
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`17`

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`text(Perimeter of 1 triangle = 3 cm.)`

`text(Add a square,)`

`text(Perimeter increases by 2 cm = 5 cm)`

`text(Add a triangle,)`

`text(Perimeter increases by 1 cm = 6 cm)`
 

`:.\ text(Perimeter of 5 triangles and 5 squares)`

`=3+2+1+2+1+2+1+2+1+2`

`=17\ text(cm)`