Architecture and Mathematics(in progress)
An architect is a person who designs buildings, prepares structures (blueprints), and manages construction.
How math apply's to architecture: - Geometry: Conversions(unit of measurement) when buying supply from the US for example. Optimizing space(volume) - Finance: budgets and costs (products from other places).Exchange rate and net income (revenue-expenses). - Algebra: ax^2+bx+c parabola (how high a building can be) - 1-variable stat: Inflation of costs (labor or material)
Problems and Solutions
You are an architect hired by a family to design a small 1 story house with 2 bedrooms, 2 baths, kitchen, dining room, and living room. The size of the house will be 34ft by 24ft. They also would like an estimate on cost of material for shingles on the roof and vinyl siding. All materials must be bought in the US and converted to Canadian dollars.
1)What is the area and perimeter of the house as a whole?
perimeter of house: 2l+2w 2(24)+2(36) 48+72 =120ft
Area of house: lxw 36x24 =864ft^2
2)What is the area of each room on the plan and the hallway (as one space)?
Living room: 18x12=216ft^2 Bathroom+laundry: 9x9=81ft^2 Bedroom: 9x9=81ft^2 Kitchen: 12x7.5=90ft^2 Dining room: 10.5x9=94.5ft^2 Ensuite bathroom: 9x6=54ft^2 Master bedroom: 9x12=108ft^2
Hallway: 81+31.5+27= 139.5ft^2
3)If the average cost of shingles is $5.11/per square foot, how much will it cost to put shingles on the roof?
roof 3: a^2+b^2=c^2 18^2+b^2=19.21^2 324+b^2=369.02 b^2=369.02-324 (square root) b=6.70
Area: \(\frac{18x6.7}{2}\) =120.6ft^2
roof 1: 9^2+12^2=C^2 81+144=C^2 C^2=225 (square root) c=15ft
15^2+12^2=c^2 c^2=225+144 C^2=369 (square foot) c=19.21 area: \(\frac{12x13 }{2}\) =180ft^2