1. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter 4 4 Sample Questions & Solutions

2. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter Take 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 floor25m² So Area of floor = 5 x 5 = 25m² carpet19.625m² Area of carpet = πr² = 3.14 x 2.5² = 19.625m² So area of the flooring required = area of floor – area of carpet = 25 – 19.625 = 5.375m²

3. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & 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. (*roof surface to both pitches) Area of roof surface = (12 x 4.1) x 2 (*roof surface to both pitches) 98.4m² = 49.2 x 2 = 98.4m² Number of tiles = 98.4 x 11 = 1,082.4 1,083 or 1,083 to nearest tile Roof felt = 98.4 ÷ 50 = 1.968 2 Rolls or 2 Rolls to the nearest full roll

4. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & 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 2 We are looking for the area of 2 gables we can drop the division Therefore Base x Height (B x H) will give us the area for both gables 24m² So 5 x 4.8 = 24m² For cladding 24 ÷ 0.098 (cladding width in meters) 245m (to nearest m) = 244.898 or 245m (to nearest m) 4.8m 5m A

5. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter 3m 2m 3m 3.4m 3m 4m Exercise Calculate Floor Perimeter for skirting Calculate Floor Area for flooring material

6. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter 3m 2m 3m 3.4m 3m 4m Perimeter For Perimeter 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

7. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter 3m 2m 3m 3.4m 3m 4m So Perimeter is 3+3+3.4+3+3 +3+3+3+3+3+3+2+3+3+3+3+3+3+2 +3+5.3414+3 +7+5+7+5 = 58.7414m Point A

8. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter 3m 2m 3m 3.4m 3m 4m S S R SC T separate For Area separate the shapes on the plan, apply the relevant formulae and then calculate the sum total R In this example we have 1 Rectangle R S + 2 Squares S T + 1 Triangle T SC + 1 Semi-circle SC So Area = the sum of the areas of R + S + S +T + SC

9. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter 3m 2m 3m 3.4m 3m 4m S S R SC T R R = L x B 103.4 = 11 x 9.4 = 103.4 S S = L x B = 3 x 3 = 9 18 x 2 = 18 T6 T = B x H = 3 x 4 = 6 2 2 SC SC = πr² = 3.14 x 1.7² 2 2 4.54 = 4.54 = 103.4 + 18 + 6 + 4.54 = 131.94m²

10. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter In some instances we may be asked to calculate the material required to cover the floor area. Example Example: Calculate the number of sheets of plywood sheets to floor this area 2440mm x 1220mm Plywood: 2440mm x 1220mm

11. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter 131.94m² Area of floor = 131.94m² (from previous calculation) Area of Plywood = 2.44 x 1.22 = 2.9768m² Number of sheets required = Area of floor ÷ Area of Plywood =131.94 ÷ 2.9768 = 44.32 = 45 sheets to the nearest full sheet

12. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter In some instances we may be asked to calculate the flooring required in linear meters. Example Example: Calculate the linear meters of floorboards required to cover this floor 125mm x 22mm Floorboard: 125mm x 22mm

13. Carpentry & Joinery Phase 4 Module 1 Unit 5 Area & Perimeter 131.94m² Area of floor = 131.94m² (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) 1,056m = 1,055.52 or 1,056m