Unit 9. Day 4.

So far we’ve noticed this pattern: Scale factor: 2 10 m 10 m 5 m 5 m 4 m 4 m 2 m 2 m 40 𝑚 2 40 𝑚 2 10 𝑚 2 10 𝑚 2 14 m 28 m 2 1 2 1 2 1 4 1

You will tackle some (in my opinion) challenging problems that use this idea: 4 3 Scale factor: Side Area Original Scale Drawing 4 3 16 9 Groups of 4

Example A:Based on the drawing below, what will the area of the planned half-court be? Scale Drawing: 1 in. on the drawing corresponds to 15 ft. of actual length 10 𝑚𝑖𝑛𝑢𝑡𝑒𝑠

Example A:Based on the drawing below, what will the area of the planned half-court be? Scale Drawing: 1 in. on the drawing corresponds to 15 ft. of actual length 2 1 𝑖𝑛 5 3 𝑖𝑛 2 𝐴= 15 𝑓𝑡 1 𝑖𝑛 𝑙𝑒𝑛𝑡ℎ 2 𝑖𝑛 𝑤𝑖𝑑𝑡ℎ 𝑆𝑐𝑎𝑙𝑒 ( ): 𝑎𝑟𝑒𝑎 𝑠𝑖𝑑𝑒 10 3 𝐴= 𝑖𝑛 2 225 𝑓𝑡 2 1 𝑖𝑛 2 𝑆𝑐𝑎𝑙𝑒 (𝑎𝑟𝑒𝑎): 10 3 225 𝑓𝑡 2 1 𝑖𝑛 2 𝐴= ∙ 𝑖𝑛 2 2250 𝑓𝑡 2 𝐴= 750 3

Example A:Based on the drawing below, what will the area of the planned half-court be? Scale Drawing: 1 in. on the drawing corresponds to 15 ft. of actual length = 15 𝑓𝑡 𝑥 𝑓𝑡 𝐴= 30 𝑓𝑡 𝑙𝑒𝑛𝑡ℎ 25 𝑓𝑡 𝑤𝑖𝑑𝑡ℎ 1 𝑖𝑛 2 𝑖𝑛 𝐴= 750 𝑓𝑡 2 1𝑥 = 30 𝑓𝑡 30 15 𝑓𝑡 = 𝑥 𝑓𝑡 1 𝑖𝑛 5 3 𝑖𝑛 1𝑥 = 25 𝑓𝑡 25

Example B: The triangle depicted by the drawing has an actual area of 36 square units. What is the scale of the drawing? (Note: Each square on the grid has a length of 1 unit.) 10 𝑚𝑖𝑛𝑢𝑡𝑒𝑠

Example B: The triangle depicted by the drawing has an actual area of 36 square units. What is the scale of the drawing? (Note: Each square on the grid has a length of 1 unit.) 6 1 2 Scale factor: 𝐴= 2 6 3 𝑏𝑎𝑠𝑒 ℎ𝑒𝑖𝑔ℎ𝑡 𝐴= 18 2 =9 𝐴𝑟𝑒𝑎 𝑆𝑖𝑑𝑒 3 𝑠𝑐𝑎𝑙𝑒 𝑑𝑟𝑎𝑤𝑖𝑛𝑔 𝑎𝑐𝑡𝑢𝑎𝑙 : 9 36 1 2 3 6 6

N/A Scale Factor 16 6 ? 48 𝑢𝑛𝑖𝑡𝑠 2 28 10 ? 140 𝑢𝑛𝑖𝑡𝑠 2 𝑠𝑚𝑎𝑙𝑙 𝑙𝑎𝑟𝑔𝑒 = Base Height Perimeter Area Small Large Scale Factor 16 6 ? 48 𝑢𝑛𝑖𝑡𝑠 2 28 10 ? 140 𝑢𝑛𝑖𝑡𝑠 2 N/A 𝑠𝑚𝑎𝑙𝑙 𝑙𝑎𝑟𝑔𝑒 = 4 7 3 5 48 140 ? ? 24 70 12 35 10 6 16 28 Example C: