Maths Quest A year 11 for Queensland
WorkSHEET 8.2
Chapter 8 Construction: the finishing touches WorkSHEET 8.2
1
Construction: the finishing touches
Name: ___________________________
Questions 1 – 6 refer to information available from the floor plan below.
1
In the floor plan above, the small hallway
leading to the toilet, together with the toilet
area itself, must be prepared for tiling.
Use the scale of the plan, together with
measurements, to calculate this area.
This area measures 2.9 cm by 1.5 cm.
Scale is 1 : 150.
Actual measurements are
(2.9 cm  150) by (1.5 cm  150)
i.e. 4.35 m by 2.25 m
 Area = 4.35 m  2.25 m
= 9.8 m2
Maths Quest A year 11 for Queensland
Chapter 8 Construction: the finishing touches WorkSHEET 8.2
2
Estimate the cost of tiling the area in
question 1, if the tiles can be laid for $45/m2.
3
The bathroom contains a shower and a vanity
unit. Use the scale for the plan, together with
measurements, to estimate the floor area these
two objects occupy.
Area to be tiled = 9.8 m2
Tiling cost = $45/m2
 Cost of tiling hallway and toilet
= $45  9.8
= $441
The plan measurements of the vanity unit and
the shower are shown above.
Using the scale of 1 : 150, the actual
measurements are:
Vanity unit — 1.5 m by 0.75 m
Shower — 1.35 m by 1.35 m
Total area = (1.5 m  0.75 m) + (1.35 m)2
= 1.125 + 1.8225 m2
= 2.9 m2
4
Estimate the cost to tile the bathroom around
Bathroom measures 1.5 cm by 2.9 cm on the
the vanity unit and the shower with tiles costing plan (scale 1 : 150).
$45/m2 laid.
So, actual dimensions are
(1.5 cm  150) by (2.9 cm  150)
i.e. 2.25 m by 4.35 m.
Area of bathroom = 2.25 m  4.35 m
= 9.8 m2
Area occupied by vanity unit and shower
= 2.9 m2
 Area to be tiled = 9.8 m2 – 2.9 m2
= 6.9 m2
Cost to tile this area = $45  6.9
= $310.50
2
Maths Quest A year 11 for Queensland
5
Chapter 8 Construction: the finishing touches WorkSHEET 8.2
What would it cost to carpet the lounge with
3.66 m wide carpet laid parallel to the longer
side. The cost of the carpet is $120/m.
Lounge measures 4.3 m by 2.8 m.
So, length of lounge = 4.3 cm  150
= 6.45 m
Width of lounge = 2.8 cm  150
= 4.2 m
Laying the carpet parallel to the 6.45 m side
would require two strips of carpet.
 Length of carpet required = 6.45 m  2
= 12.9 m
 Cost of carpet = 12.9 m  $120/m
= $1548
6
Recalculate question 5, laying the carpet in the
lounge room parallel to the shorter side.
Compare your answers (as far as cost is
concerned).
Two strips of carpet would still be required.
However, this time the strips are each 4.2 m
long instead of 6.45 m long.
 Length of carpet required
= 4.2 m  2
= 8.4 m
 Cost of carpet = 8.4 m  $120/m
= $1008
It is cheaper to lay the carpet parallel to the
shorter side by $1548 – $1008 i.e. $540.
3
Maths Quest A year 11 for Queensland
Chapter 8 Construction: the finishing touches WorkSHEET 8.2
Questions 7 and 8 refer to information available from the front elevation of a house as shown below.
7
Use measurements together with the scale, to
Each railing measures 4.2 cm by 1.2 cm on the
determine the area occupied by the two railings plan.
at the entrance to the house.
Scale is 1 :100.
 Actual measurements of the railings are
(4.2 cm  100) by (1.2 cm  100)
i.e. 4.2 m by 1.2 m.
 Area of two sets of railings
= (4.2  1.2)  2 m2
= 10.08 m2
8
The timber for the railings can bed purchased,
cut to size, for $1.40 per linear metre.
Determine the length of timber required, then
calculate the cost per square metre for the
railings.
Railing lengths from plan
4  4.2 cm = 16.8 cm
+ 28  1.1 cm = 30.8 cm
Total = 47.6 cm
Using scale 1 : 100, this represents a length of
47.6 m.
Cost of timber = $1.40  47.6
= $66.64
The railings cover an area of 10.08 m2 (from
question 7).
 Cost per square metre = $66.64  10.08
= $6.61
4
Maths Quest A year 11 for Queensland
Chapter 8 Construction: the finishing touches WorkSHEET 8.2
For questions 9 and 10, refer to the information contained in the site plan below.
9
Use the scale of the plan to determine the
dimensions of the shed in the northern corner
of the block of land.
The shed is square, measuring 2.3 cm on the
plan.
Scale is 1 : 250.
 Dimensions of the shed are
2.3 cm  250 i.e. 5.75 m square.
5
Maths Quest A year 11 for Queensland
10
Chapter 8 Construction: the finishing touches WorkSHEET 8.2
The roof of the shed is the same style as that of
the house depicted in questions 7 and 8.
It is a hip roof with the four faces meeting at
the apex. Its pitch angle is 20  .
Determine the area of the roof.
1
 5.75 m
2
 2.875 m
In ABC, BC 
ABC  20  (pitch angle )
adj.
hyp.
2.875

AC
cos 20  
AC  cos 20   2.875
2.875
AC 
cos 20 
 3.1 m
AC is the perpendicular height of the triangle
ADE.
The four triangular roof faces are all the same
size.
bh
4
2
5.75  3.1

4
2
 Area of roof 
 35.65 m 2
6