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v1 Measurement, STD2 M1 2009 HSC 23c

The diagram shows the shape and dimensions of a floor which is to be tiled.
 

  1. Find the area of the floor.   (2 marks)

  2. Tiles are sold in boxes. Each box holds one square metre of tiles and costs $60. When buying the tiles, 10% more tiles are needed, due to cutting and wastage.

     

    Find the total cost of the boxes of tiles required for the floor.   (2 marks)

Show Answers Only

i.    `17\ text(m²)`

ii.   `$1140`

Show Worked Solution
i.
`text(Area)` `=\ text(Area of big square – Area of 2 cut-out squares`
  `= (3 + 2) xx (3 + 2)\-2 xx (2 xx 2)`
  `= 25\-8`
  `= 17\ text(m²)`

 

ii. `text(Tiles required)` `= (17 +10 text{%}) xx 17`
    `= 18.7\ text(m²)`

 

 `=>\ text(19 boxes are needed)`

`:.\ text(Total cost of boxes)` `=19 xx $60`
  `= $1140`

Area, SMB-029 MC

The plan of a square area of land is drawn below.

A mining licence is granted over part of the land.

All measurements are given in kilometres.
 

The area of land the mining licence covers is

  1. `x^2-20`
  2. `x^2 + 20`
  3. `2x^2-9`
  4. `2x^2-20`
Show Answers Only

`A`

Show Worked Solution

`text{Area of original land}\ = x xx x = x^2\ text{km}^2`

`text{Size of non-mining area}\ = 4 xx 5 = 20\ text{km}^2`

`:.\ text(Area of mining)\ = (x^2-20)\ text{km}^2`

`=>A`

Area, SMB-027

Kate owns a farm with a square paddock. She increases the area of the paddock by changing it into the shape of trapezium.
 

What is the area of the new paddock, in square metres?   (2 marks)

Show Answers Only

`1505\ text(m²)`

Show Worked Solution
`A` `= 1/2h(a + b)`
  `= 1/2 xx 35 xx (35 + 51)`
  `= 1505\ text(m²)`

Area, SMB-025

An irregular shaped lawn is pictured below, with all measurements in metres.
  

 

What is the area of the lawn in square metres?   (3 marks)

Show Answers Only

`65\ \text{m}^2`

Show Worked Solution

`text(Split the lawn into 3 areas)`

`text(Area 1) = 9 xx 3 = 27\ text(m²)`

`text(Area 2) = 5 xx 2 = 10\ text(m²)`

`text(Area 3:)`

`text(Height) = 5+2 = 7\ text(m)`

`text(Width)= 12-(5 + 3)= 4\ text(m)`

`=> text(Area 3) = 7 xx 4 = 28\ text(m²)`

 

`:.\ text(Area of lawn)` `= 27 + 10 + 28`
  `= 65\ text(m²)`

Area, SMB-024

A plan of Zev's backyard is shown.
  

 

Zev wants to fertilise the lawn in his backyard and needs to know the total area.

What is the total area of Zev's lawn, in square metres?   (2 marks)

Show Answers Only

`text(26 m²)`

Show Worked Solution

`text(Area)` `=\ text(square + triangle)`
  `= (4 xx 4) + (1/2 xx 4 xx 5)`
  `= 16 + 10`
  `= 26\ text(m²)`

Area, SMB-023 MC

Harry has an irregularly shaped back yard.
  

What is the area of Harry's back yard?

  1. `text(93 m)²`
  2. `text(384 m)²`
  3. `text(544 m)²`
  4. `text(768 m)²`
Show Answers Only

`B`

Show Worked Solution
`text(Area)` `= (1/2 xx 14 xx 32) + (1/2 xx 10 xx 32)`
  `= 224 + 160`
  `= 384\ text(m)²`

 
`=>B`

Area, SMB-021 MC

Pablo cuts a square out of a rectangular piece of paper, as shown below.

The square Pablo cut out has a side length of 6 cm.

Which of these expressions gives the area of Pablo's piece of paper after cutting out the square?

  1. `(28 xx 20)-(6 xx 6)`
  2. `(22 xx 14) + (6 xx 6)`
  3. `(28 + 20)-(6 + 6)`
  4. `(28 + 20) + (6 xx 6)`
Show Answers Only

`A`

Show Worked Solution
`text(Area)` `=\ text(Area of larger rectangle − Area of square)`
  `= (28 xx 20)-(6 xx 6)`

 
`=>A`

Area, SMB-020

A trapezium is constructed on a grid of 10 rectangles.

Each rectangle measures  3 cm × 7 cm.

 

Find the area of the trapezium?   (2 marks)

Show Answers Only

`168\ text(cm²)`

Show Worked Solution
`text(Area 1 rectangle)` `= 3 xx 7`
  `= 21\ text(cm²)`

 

`:.\ text(Total Area)` `= (6 xx 21) + 2\ text(triangles)`
  `= 6 xx 21 + 2 xx (1/2 xx 3 xx 14)`
  `= 126 + 42`
  `= 168\ text(cm²)`

Area, SMB-019 MC

Olive drew this plan of her lawn.

Which expression gives the area of Olive's lawn?

  1. `(a xx b) + (c xx d)`
  2. `(a xx b) xx (c xx d)`
  3. `(a + b) + (c + d)`
  4. `(a + b) xx (c + d)`
Show Answers Only

`A`

Show Worked Solution

`text(Total Area)` `= text(Area 1) + text(Area 2)`
  `= (a xx b) + (c xx d)`

`=> A`

Area, SMB-007

The diagram shows the shape of Carmel’s garden bed. All measurements are in metres.
  

Show that the area of the garden bed is 57 square metres.  (2 marks)

Show Answers Only

`text(Proof)\ \ text{(See Worked Solutions)}`

Show Worked Solution
`text(Area of)\ Delta ABC` `= 1/2 xx b xx h`
  `= 1/2 xx 10 xx 5.1`
  `= 25.5\ text(m²)`
`text(Area of)\ Delta ACD` `= 1/2 xx 10 xx 6.3`
  `= 31.5\ text(m²)`

 

`:.\ text(Total Area)` `= 25.5 + 31.5`
  `= 57\ text(m² … as required)`

Area, SMB-028

 

What is the area of the shaded part of the figure?   (2 marks)

Show Answers Only

`8.5\ text(cm)^2`

Show Worked Solution

`text(Area of large triangle)`

`= 1/2 xx 5 xx 5`

`= 12.5\ text(cm)^2`

`text(Area of smaller triangle)`

`= 1/2 xx 2 xx 2`

`= 2\ text(cm)^2`

 

`:.\ text(Shaded area)`

`= 12.5-(2 xx 2)`

`= 8.5\ text(cm)^2`

Measurement, STD2 M1 2009 HSC 23c

The diagram shows the shape and dimensions of a terrace which is to be tiled.
 

  1. Find the area of the terrace.   (2 marks)

  2. Tiles are sold in boxes. Each box holds one square metre of tiles and costs $55. When buying the tiles, 10% more tiles are needed, due to cutting and wastage.

     

    Find the total cost of the boxes of tiles required for the terrace.   (2 marks)

Show Answers Only

i.    `13.77\ text(m²)`

ii.   `$880`

Show Worked Solution
i.
`text(Area)` `=\ text(Area of big square – Area of 2 cut-out squares`
  `= (2.7 + 1.8) xx (2.7 + 1.8)\-2 xx (1.8 xx 1.8)`
  `= 20.25\-6.48`
  `= 13.77\ text(m²)`

 

ii. `text(Tiles required)` `= (13.77 +10 text{%}) xx 13.77`
    `= 15.147\ text(m²)`

 

 `=>\ text(16 boxes are needed)`

`:.\ text(Total cost of boxes)` `=16 xx $55`
  `= $880`