smc-1105-10-Floor Plans

Measurement, STD1 M5 2025 HSC 26

A scale of $1 : 50$ is used to draw a rectangular area on a 2 mm grid as shown. The actual rectangular area is to be tiled.

The tiles cost $150 per square metre and the tiler orders 15% extra tiles to allow for cutting and breakage.

The tiler charges $90 per hour and will take 20 hours to complete the tiling.

Calculate the total cost of the tiles and tiling. Give your answer to the nearest dollar. (4 marks)

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$$6105.60$

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$\text{Using scale where each grid is 2mm × 2 mm:}$

$2\ \text{mm}\ =50 \times 2 = 100\ \text{mm in actual length}$

$\text{100 mm = 10 cm}$

$\Rightarrow \ \text{i.e. each grid represents 10 cm in actual length.}$

$\text{Width}\ = 52 \times 10 = 520\ \text{cm}\ = 5.2\ \text{m}$

$\text{Height}\ = 48 \times 10 = 480\ \text{cm}\ = 4.8\ \text{m}$

$\text{Area}=5.2 \times 4.8=24.96\ \text{m}^2$

$\text{Cost of tiles}=24.96\times $150\times 1.15=$4305.60$

$\text{Labour Cost}=90\times 20=$1800$

$\therefore\ \text{Total Cost}=$4305.60+$1800=$6105.60$

Measurement, STD1 M5 2024 HSC 29

A floor plan for a living area is shown. All measurements are in millimetres.

What is the length and width of the cupboard, in metres? (1 mark)

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The floor of the living area is to be tiled. Tiles will NOT be placed under the cupboard.
Each tile is 0.2 m × 0.5 m. The tiles are supplied in boxes of 15 at a cost of $100 per box. Only full boxes can be purchased.
What is the cost of the tiles for the living area? (4 marks)
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a. $4\ \text{m}\times 0.5\ \text{m}$

b. $$1100$

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a. $\text{1 metre = 1000 mm}$

$\text{Cupboard}\ = 4\ \text{m}\times 0.5\ \text{m}$

Mean mark (a) 53%.

b. $\text{Method 1}$

$\text{Total area to be tiled}\ =6\times 3-4\times 0.5=16\ \text{m}^2$

$\text{Area of each tile}\ =0.2\times0.5=0.1\ \text{m}^2$

$\text{Tiles needed}\ =\dfrac{16}{0.1}=160\ \text{tiles}$

$\text{Number of boxes}\ =\dfrac{160}{15}=10.66\dots=11\ \text{boxes}$

$\therefore\ \text{Total cost}\ =100\times 11=$1100$

$\text{Method 2}$

$\text{Tiles to fit 6 m width}\ =\dfrac{6}{0.2}=30 $

$\text{Tiles to fit 2 m width}\ =\dfrac{2}{0.2}=10 $

$\text{Total tiles}\ =30\times 5\ \text{rows}+10\times 1\ \text{rows}\ =160$

$\text{Number of boxes}\ =\dfrac{160}{15}=10.66\dots=11\ \text{boxes}$

$\therefore\ \text{Total cost}\ =100\times 11=$1100$

♦♦ Mean mark (b) 35%.

Measurement, STD1 M5 2022 HSC 11

The floor plan of a home unit has been drawn to scale.

How many doors are shown on the plan? (1 mark)

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What is the total floor area of the home unit in square metres? (2 marks)

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`5`
`text{55.5 m²}`

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a. `5`

b. `text{Conversion: 1000 mm = 1 metre}`

`text{Calculate area by splitting into 2 rectangles}`

`text{Area}`	`= 5.5 × 5 + (4.5 +2.5) xx 4`
	`= 55.5\ text{m²}`

♦♦ Mean mark part (b) 26%.

Measurement, STD1 M5 2021 HSC 24

A building plan of part of a house is shown.

What is the internal length and the internal width of the main bedroom? Give your answer in metres. (1 mark)

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Rod wants to lay carpet in the main bedroom. The main bedroom has a wardrobe with a base area of 1.6 m². The area under the wardrobe does NOT need to be carpeted.
Carpet costs $40 per square metre. Rod buys the smallest whole number of square metres of carpet necessary. Find the cost of the carpet purchased for the bedroom. (3 marks)

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`3.6\ text(metres)`
`$680`

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a. `text(Internal length = 5000 mm = 5 metres)`

♦ Mean mark part (a) 46%.

`text(Internal width = 3600 mm = 3.6 metres)`

♦♦ Mean mark part (b) 30%.

b.	`text(Carpet area)`	`= (5 xx 3.6) – 1.6`
		`= 16.4\ text(m²)`
		`= 17\ text{m² (round up)}`

`text(C)text(ost of carpet)`	`= 17 xx 40`
	`= $680`

Measurement, STD1 M5 2020 HSC 23

The diagram shows a scale drawing of the floor of a room.

Carpet is to be laid to cover the entire floor. The cost of the carpet is $100 per square metre.

Find the total cost of the carpet required. (3 marks)

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`$9000`

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`text{Ratio of sides}`	`= \ text{base : height}`
	`=8 : 5`

`text{Find actual} \ h :`

COMMENT: Note the image dimensions on the actual HSC paper were exactly 8 cm × 5 cm, making this ratio easy to calculate.

`frac{h}{12}`	`= frac{5}{8}`
`h`	`= frac{5 xx 12}{8} = 7.5`

♦ Mean mark 41%.

`text{Area (actual)} = 12 xx 7.5 = 90 \ text{m}^2`

`therefore \ text{C} text{ost}`	`= 90 xx 100`
	`= $9000`

Measurement, STD1 M5 2019 HSC 20

The plan of the lower level of a small house is shown.

How many windows are shown on the plan? (1 mark)

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What is the actual perimeter, in metres, of the shaded part of the kitchen floor? (2 marks)

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`text(6 windows)`
`6.5\ text(metres)`

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a. `text(6 windows)`

b.	`text(Plan Perimeter)`	`= 2 xx 3\ text(units) + 2 xx 3.5\ text(units)`
		`= 13\ text(units)`

`:.\ text(Actual perimeter)`	`= 13 xx 0.5`
	`= 6.5\ text(metres)`

Measurement, STD2 M7 2015 HSC 29c

The image shows a rectangular farm shed with a flat roof.

The real width of the shed indicated by the dotted line was measured using an online ruler tool, and found to be approximately 12 metres.

By measurement and calculation, show that the area of the roof of the shed is approximately 216 m². (2 marks)

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All the rain that falls onto this roof is diverted into a cylindrical water tank which has a diameter of 3.6 m. During a storm, 5 mm of rain falls onto the roof.

Calculate the increase in the depth of water in the tank due to the rain that falls onto the roof during the storm. (3 marks)

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`text(See Worked Solutions.)`
`10.6\ text{cm (to 1 d.p.)}`

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i. `text(By measurement,)`

♦ Mean mark 35%.

`text(Roof length = 1.5 times the roof width)`

`text{Width = 12 m (given)}`

`text(Length)`	`= 1.5 xx 12`
	`= 18\ text(m)`

`:.\ text(Area of roof)`	`= 12 xx 18`
	`= 216\ text(m²)\ \ text(…as required)`

ii. `text(Volume of water)`

♦♦♦ Mean mark 14%.

`= Ah`

`= 216 xx 0.005\ \ \ (5\ text(mm) = 0.005\ text(m))`

`= 1.08\ text(m³)`

`text(Volume of cylinder =)\ pir^2h`

`r = 3.6/2 = 1.8\ text(m)`

`text(Find)\ h\ text(when)\ V= 1.08\ text(m³),`

`pi xx 1.8^2 xx h`	`= 1.08`
`:. h`	`= 1.08/(pi xx 1.8^2)`
	`= 0.1061…\ text(m)`
	`= 10.6\ text{cm (to 1 d.p.)}`

Measurement, STD2 M7 2011 HSC 24a

Part of the floor plan of a house is shown. The plan is drawn to scale.

What is the width of the stairwell, in millimetres? (1 mark)

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What are the internal dimensions of the bathroom, in millimetres? (1 mark)

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What is the length `AB`, the internal length of the rumpus room, in millimetres? (1 mark)

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`900\ text(mm)`
`2000\ text(mm) xx 2000\ text(mm)`
`9695\ text(mm)`

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i.	`900\ text(mm)`

ii.

`2000\ text(mm) xx 2000\ text(mm)`

iii.

`text(Length of Rumpus Room) = AB`

`AB`	`= 3600 + 90 + 2000 + 90 + 3915`
	`=9695\ text(mm)`

Measurement, STD2 M7 2010 HSC 23b

The elevation and floor plan of a building are shown.

Calculate the area of the floor of this building in square metres. (2 marks)

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`46\ text(m²)`

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MARKER’S COMMENT: Less errors were made by students who converted to metres FIRST, before calculating the area.

`text(Floor Area)`	`=text(Area)\ 1+text(Area)\ 2`
	`=(8xx5)+(2xx3) \ \ \ \ text{(1 m = 1000 mm)}`
	`=46\ text(m²)`