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Area & PerimeterArea & Perimeter4
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Sample Questions & Sample Questions & SolutionsSolutions
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Area & PerimeterArea & PerimeterTake an example of a timber floor project where a central circular area is to be carpeted and we must calculate the remaining area for flooring.
The information we are given is that we have a square floor area with a length of 5m. Firstly we must establish the floor area and then deduct the carpeted area to find the area of flooring required. 5 m
So Area of floorfloor = 5 x 5 = 25m²25m² Area of carpetcarpet = πr² = 3.14 x 2.5² = 19.625m²19.625m²So area of the flooring required = area of floor – area of carpetSo area of the flooring required = area of floor – area of carpet= 25 – 19.625 = 5.375m² = 25 – 19.625 = 5.375m²
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Area & PerimeterArea & Perimeter
4.1m
12m
Calculate the number of roof tiles and rolls of roof felt required to cover the double pitched shown in the diagram given that coverage of the roof tiles is 11tiles per m² and roof felt is 50m² per roll.
Area of roof surface = (12 x 4.1) x 2 (*roof surface to both pitches)(*roof surface to both pitches)= 49.2 x 2 = 98.4m² 98.4m² Number of tiles = 98.4 x 11 = 1,082.4 or 1,083 1,083 to nearest tileRoof felt = 98.4 ÷ 50 = 1.968 or 2 Rolls 2 Rolls to the nearest full roll
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Area & PerimeterArea & Perimeter
4.1m
12m
Calculate in linear meters the quantity of Red Cedar horizontal cladding required to cover both gables (A) of the double pitched roof shown.Cladding: 98mm x 18mm
Our given formula for area of a triangle is Base x Height divided by 2We are looking for the area of 2 gables we can drop the divisionTherefore Base x Height (B x H) will give us the area for both gablesSo 5 x 4.8 = 24m²24m²For cladding 24 ÷ 0.098 (cladding width in meters) = 244.898 or 245m245m (to nearest m) (to nearest m)
4.8m
5m
A
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Area & PerimeterArea & Perimeter
3m 3m 3m 2m
3m
3m
3.4m
3m
3m4m
ExerciseExercise
Calculate Floor Perimeter for skirting
Calculate Floor Area for flooring material
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Area & PerimeterArea & Perimeter
3m 3m 3m 2m
3m
3m
3.4m
3m
3m4m
For PerimeterPerimeter pick a starting point and work clockwise adding the sum of your running measurements
First calculate the length of the semi-circular line ie. πr 3.142 x 1.7 = 5.3414
Then the length of the hypotenuse of the triangle ie. 5 (3,4,5 Rule)
Point A
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Area & PerimeterArea & Perimeter
3m 3m 3m 2m
3m
3m
3.4m
3m
3m4m
So Perimeter is3+3+3.4+3+3+3+3+3+3+3+3+2+3+5.3414+3+7+5 = 58.7414m
Point A
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Area & PerimeterArea & Perimeter
3m 3m 3m 2m
3m
3m
3.4m
3m
3m4m
SS SS
RRSCSC
TT
For Area separateseparate the shapes on the plan, apply the relevant formulae and then calculate the sum total
In this example we have 1 Rectangle RR+ 2 Squares SS+ 1 Triangle TT+ 1 Semi-circle SCSC
So Area = the sum of the areas ofR + S + S +T + SCR + S + S +T + SC
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Area & PerimeterArea & Perimeter
3m 3m 3m 2m
3m
3m
3.4m
3m
3m4m
SS SS
RRSCSC
TT
RR = L x B = 11 x 9.4 = 103.4103.4
S S = L x B = 3 x 3 = 9 x 2 = 1818
TT = B x H = 3 x 4 = 66 2 2
SCSC = πr² = 3.14 x 1.7² 2 2 = 4.544.54
= 103.4 + 18 + 6 + 4.54= 103.4 + 18 + 6 + 4.54
= = 131.94m²131.94m²
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Area & PerimeterArea & Perimeter
In some instances we may be asked to calculate the material required to cover the floor area.
ExampleExample: Calculate the number of sheets of plywood sheets to floor this area
Plywood: 2440mm x 1220mm2440mm x 1220mm
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Area & PerimeterArea & Perimeter
Area of floor = 131.94m² 131.94m² (from previous calculation)(from previous calculation)
Area of Plywood = 2.44 x 1.22= 2.9768m²= 2.9768m²
Number of sheets required = Area of floor ÷ Area of Plywood =131.94 ÷ 2.9768 = 44.32=131.94 ÷ 2.9768 = 44.32
= = 45 sheets 45 sheets to the nearest full to the nearest full sheetsheet
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Area & PerimeterArea & Perimeter
In some instances we may be asked to calculate the flooring required in linear meters.
ExampleExample: Calculate the linear meters of floorboards required to cover this floor
Floorboard: 125mm x 22mm125mm x 22mm
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Area & PerimeterArea & Perimeter
Area of floor = 131.94m² 131.94m² (from previous calculation)(from previous calculation)
Divide floor area by floorboard width (NB* flooring thickness is not relevant to this calculation, we are only interested in the face of the board for area)
131.94 ÷ 0.125 (width in meters)= 1,055.52 or 1,056m 1,056m
