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v1 Measurement, STD1 M5 2021 HSC 26

The diagrams show two similar shapes. The dimensions of the small shape are enlarged by a scale factor of 1.5 to produce the large shape.
 

Calculate the area of the large shape.  (3 marks)

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`94.5\ text(cm)^2`

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`text(Dimension of larger shape:)`

♦♦ Mean mark 32%.

`text(Width) = 6 xx 1.5 = 9\ text(cm)`

`text(Height) = 8 xx 1.5 = 12 \ text(cm)`

`text(Triangle height) = 2 xx 1.5 = 3\ text(cm)`

`:.\ text(Area)` `= 9 xx (12-3) + 1/2 xx 9 xx 3`
  `= 94.5\ text(cm)^2`

Similarity, SMB-011

Kransky has a photo which is 25 cm wide and 10 cm high

He wants to enlarge it to make a poster with a width of 50 cm.

What will be the height of the poster?   (2 marks)

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`text(20 cm)`

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`text(Scale factor)` `= text(new width)/text(old width)`
  `= 50/25`
  `= 2`

 

`:.\ text(New height)` `= 2 xx 10`
  `= 20\ text(cm)`

Similarity, SMB-009

Juanita wanted to print a larger copy of her photo of a tree.

She increased the scale by a factor of 3.

She named the first picture Photo A and the second picture Photo B.
 

 If Photo B is 3.2 cm high, how high is Photo A in centimetres, correct to 1 decimal place?    (2 marks)

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`1.1\ text(cm)`

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`text{Since Photo B is increased by a factor of 3,}`

`text(Height of Photo B)/text(Height of Photo A)` `=3`
`:.\ text(Height of Photo A)` `=text(Height of Photo B)/3`
  `=3.2/3`
  `=1.0666…`
  `=1.1\ text{cm  (1 d.p.)}`

Similarity, SMB-007

Two circles have the same centre, `O`, as shown in the diagram below.
 

The radius of the small circle is  `2/3`  the radius of the large circle.

Arc `CD` is 21 cm and the angle between the lines `AC` and `BD` is 45°.

What is the length of the arc `RS` in centimetres?   (3 marks)

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`text(42 cm)`

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`text{Circles are similar}`

`text(Arc)\ ST` `= 2/3 xx text(arc)\ CD`
  `= 2/3 xx 21`
  `= 14\ text(cm)`

 

`angleSOR` `= 180-45`
  `= 135^@`
  `= 3 xx angleSOT`

 

`:. text(Arc)\ RS` `= 3 xx text(arc)\ ST`
  `= 3 xx 14`
  `= 42\ text(cm)`

Similarity, SMB-005

Trapeziums `ABCD` and `AEFG` are similar.
 

What is the distance from `E` to `F`?   (2 marks)

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`2\ text(m)`

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`text{Since trapeziums are similar:}`

`(EF)/(BC)` `= (AG)/(AD)`
`(EF)/8` `= 3/12`
`EF` `= (3 xx 8)/12`
  `= 2\ text(m)`

Measurement, STD1 M5 2022 HSC 5 MC

Two similar figures are shown.
 

What is the value of `x` ?

  1. 6
  2. 8
  3. 18
  4. 27
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`C`

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`text{Scale factor}\ =3/2 =1.5`

`:.\ x = 1.5 xx 12 = 18`
  

`text{Alternate solution}`

`text{Using sides of similar figures in the same ratio:}`

`x/12` `=3/2`  
`x` `=12 xx (3/2)`  
`x` `=18`  

   
`=> C`

Measurement, STD1 M5 2021 HSC 26

The diagrams show two similar shapes. The dimensions of the small shape are enlarged by a scale factor of 1.5 to produce the large shape.
 


 

Calculate the area of the large shape.  (3 marks)

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`279\ text(cm)^2`

Show Worked Solution

`text(Dimension of larger shape:)`

♦♦ Mean mark 32%.

`text(Width) = 16 xx 1.5 = 24\ text(cm)`

`text(Height) = 9 xx 1.5 = 13.5\ text(cm)`

`text(Triangle height) = 2.5 xx 1.5 = 3.75\ text(cm)`

`:.\ text(Area)` `= 24 xx (13.5-3.75) + 1/2 xx 24 xx 3.75`
  `= 279\ text(cm)^2`