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Measurement, NAP-L4-CA38

Josh used six identical triangular tiles to form a regular hexagon.

Each tile has an area of 4.8 cm².
 


 

Josh then adds more tiles to make a hexagon with double the side length of this hexagon.

What will be the area of this larger hexagon?

 
 
 
 
`9.6\ text(cm²)` `28.8\ text(cm²)` `57.6\ text(cm²)` `115.2\ text(cm²)`
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`115.2\ text(cm²)`

Show Worked Solution

`text(Area of 1 triangle) = 4.8\ text(cm²)`

COMMENT: If sides increase by a factor of 2 (i.e. double), area increases by a factor of 4.

`text(Area of triangle with double side length)`

`= 4 xx 4.8`

`= 19.2\ text(cm²)`
 

`:.\ text(Area of larger hexagon)`

`= 6 xx 19.2`

`= 115.2\ text(cm²)`

Number, NAP-B4-CA11

Michelle is tiling a walkway that is 5.6 metres long.

She is using cement tiles that are 0.08 metres wide.

There are no gaps between the tiles.
 

 
How should Michelle calculate how many cement tiles she will need?

 
 `5.6 ÷ 0.08`
 
 `0.08 ÷ 5.6`
 
 `5.6 xx 0.08`
 
 `5.6 - 0.08`
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`5.6 ÷ 0.08`

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`5.6 ÷ 0.08`

Measurement, NAP-C4-CA27 SA

Tom decided to cover a rectangular floor with tiles.

The tiles are twice as wide as they are long.

The floor is  `5 1/2`  tiles wide and  `11 1/2`  tiles long.
 

 
Using this pattern, what is the total number of tiles Tom will use to cover the floor?
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`226.5\ text(tiles)` 

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`text(Strategy 1:)`

`text(Tiles in bottom row =)\ 11 1/2`

`text(Tiles in top rows)` `=5 xx 23`
  `=115`

 

`:.\ text(Total tiles) = 115 + 11.5 = 126.5`

 

`text(Strategy 2:)` 

`text(Let)\ \ x= text(length of 1 tile)`

`=>\ text(Area of 1 tile)\ = 1 xx 1/2 = 1/2\ text(u²)`

`text{Area of the floor}` `= 5 1/2 xx 11 1/2`
  `=63.25\ text(u²)`

 

`:.\ text(Total tiles )` `=63.25/0.5` 
  `=126.5\ text(tiles)`

Measurement, NAP-E4-CA26

A tiler is tiling a wall that is 90 cm wide and 160 cm high.

He uses triangular tiles that are drawn below.
 

 
The tiler uses all of his tiles and has no gaps between them.

How many tiles does he need?

`200` `300` `450` `600`
 
 
 
 
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`600\ text(tiles)`

Show Worked Solution
`text(Area of wall)` `= 90 xx 160`
  `= 14\ 400\ text(cm²)`

 

`text(Area of 1 tile)` `= 1/2 xx 6 xx 8`
  `= 24\ text(cm²)`

 

`:.\ text(Tiles needed)` `= (14\ 400)/24`
  `= 600`

Measurement, NAP-G4-CA27 SA

Sam moves into a new rectangular office that measures  4.5 m × 3 m.

He decides to cover the floor with square carpet tiles.
 

 
How many boxes of carpet tiles does Sam need to order?
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`24\ text(boxes)`

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`text(Area of office in the number of tiles)`

`= 4.5/0.25 xx 3/0.25`

`= 18\ text(tiles) xx 12\ text(tiles)`

`= 216\ text(tiles)`

 

`:.\ text(Number of boxes to order)`

`= 216/9`

`= 24\ text(boxes)`

Measurement, NAP-H4-CA28 SA

A cement slab is laid in Bob's backyard that forms a 9 m × 3 m rectangle.
 

 
 

Bob is going to tile around the edge of his slab using one row of  300 mm × 300 mm tiles.

He will use 50% black tiles costing $8 per tile and 50% white tiles costing $5 per tile.

What is the total cost of the tiles he used?

$ 
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`$546`

Show Worked Solution

`text{Tiles used on length (including end tiles)}`

`= 9/0.3 + 2`

`= 32`

 

`text(Tiles used on width) = 3/0.3 = 10`

 

`:.\ text(Total tiles used)` `= 2 xx (32 + 10)`
  `= 84`

 

`:.\ text(C) text(ost)` `= (42 xx 8) + (42 xx 5)`
  `= 336 + 210`
  `= $546`