Examples:Calculations for Design A Cost of Tiles: Calculations for Design A Cost of Rails: 9 tiles x $30 for each tile 12 rails x $25 for each rail 9 x $30 = $270 12 x $25 - $300 Design Area Perimeter Cost of tiles Cost of rails Total cost A 9 square meters 12 meters $270 $300 $570 B 7 square meters 12 meters $210 $300 $510 C 9 square meters 20 meters $270 $500 $770 D 12 square meters 14 meters $360 $350 $710 E 9 square meters 14 meters $270 $350 $620 F 9 square meters 16 meters $270 $400 $670 G 11 square meters 24 meters $330 $600 $930 H 9 square meters 20 meters $270 $500 $770 I 10 square meters 16 meters $300 $400 $700 J 16 square meters 34 meters $480 $850 $1330 B. If you were the buyer for an amusement company, which design would you choose? When making your decision, you should consider both cost and design.Follow-Up 1. Of all the designs, which have an area of 9 square meters? 2. Give the price (total cost) of each design you listed in question 1. design A: $570, design C: $770, design E: $620, design F: $670, design H: $7703. What accounts for the difference in the prices of the designs you listed in question 1?
Covering & Surrounding Notes Problem 1.4 Five of the bumper-car designs in Problem 1.3 had an area of 9 square meters. You found that these designs had different prices because their perimeters were different. Questions A-E refer to the designs from Problem 1.3 A. Build a design with the same area as design G, but with a smaller perimeter. Several figures can be constructed with an area of 11 square meters and a perimeter of less than 24 meters. Possible answers: B. Design E can be made from design D by removing three tiles. You can remove the shaded squares to get design E from design D. How does the area of design D compare to the are of design E? The area of design D (12 square meters) is three more than the area of design E (9 square meters). How does the perimeter of design D compare to the perimeter of design E? C. Design F and design I have the same perimeter. Can you rearrange the tiles of design F to make design I? D. Design A and design C have the same area. Can you rearrange the tiles of design A to make design C? E. Look a design B. Can you move one tile to make a new design with a perimeter of 14 units?
Covering & Surrounding Notes Problem 3.1 The rangers in the Great Smoky Mountains National Park want to build several inexpensive storm shelters. The shelters must have 24 square meters of floor space.