Geometry Honors Area Project

You are a contractor trying to build a house for Mr. Shuler and his family. He is looking for a two story house that will fit him, his wife, and two kids, including a space for any guests he hosts over the weekends. His requirements for his house are the following:

  • Kitchen that is no smaller than 225 square feet
  • Living room that is no smaller than400 square feet
  • Dining room that is no smaller than300 square feet
  • Laundry room that is no smaller than60 square feet
  • Each child needs their own room
  • Guests will need a room to stay in while they are visiting
  • Bedrooms should be no smaller than 120 square feet
  • Bathrooms should be no smaller than the size of the laundry room
  • Each bedroom should have a closet that is no smaller than 16 square feet
  • Master bedroom, bath, and closet needs to be at least 3 times the size of a normal bedroom, bathroom, and closet
  • The garage needs to fit his and his wife’s cars (average size of 2-car garage is 400 sq. ft.)
  • First story has ceilings no lower than 12 feet
  • Second story has ceilings no lower than 10 feet
  • Each bedroom must be completely carpeted
  • Each room on the outside of the house should have at least one window and each room should be accessible through at least one entrance
  • Kitchen must have tile
  • Living and dining room must have wood floors
  • Each wall must be painted (color is up to contractor’s discretion)
  • Do not forget hallways, stairs, etc. (average width of a hallway is 3 feet)
  • The house must be at least 2,800 square feet total

It is your job to provide the most cost effective house for Mr. Shuler and his family. In competition with the other contractors designing Mr. Shuler’s house, you want to keep in mind that if you beat out the price of other contractors, Mr. Shuler will still be looking for design, accessibility, and appeal.

In addition, Mr. Shuler wants the students and staff at Sanford Middle to be impressed with his new house. Therefore, he is requiring the following shapes to be used in the making of the floor plan:

  • 2 Parallelograms that are not special
  • 5 special Parallelograms, 1 must be a rhombus
  • 2 Trapezoids
  • 1 Kite
  • 2 regular polygons where n > 4 (n = number of sides)

You may present your design on a sheet of graph paper. There needs to be a clear drawing of each room and each shape used in the making, along with the dimensions of each room. A total of the costs (per room) should be provided on a budget sheet, along with the colors and flooring being used in each room.

Costs are provided below. Remember, your goal is to be hired as the contractor to design Mr. Shuler’s house. Good luck!

Costs:

  • $125 per square foot (initial building)
  • $10 per square foot for window glass
  • $45 for each door
  • $49.25 for a box of wood floor (covers 100 square feet)
  • $32.50 for a box of floor tiling (covers 150 square feet)
  • $45 for a roll of carpet (covers 150 square feet)
  • $16.50 for a gallon of paint (normally covers about 200 square feet)
  • $4 per square foot for concrete flooring (garage)
  • $31.98 for garage floor paint (covers 150 square feet)