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Find the area of the following NONAGON, YES IT IS A NONAGON NOT AN OCTAGON!!!!!!!!!!!! 10 1 Find the sum of the interior angles of a 27­gon What is the sum of the exterior angles of a regular dodecagon? What is the measure of each interior angle of a regular 15­gon? 2 Extra problems a) 8­64 (3, 0) and (­2.5, 0) 8­65 b) same graph just flipped B 3 4 Lesson 8.2.1 How does the area change? Objective: Students will compare the area ratio for similar figures In Class Today: 8­61 When you get to part c) come up and get 8.2.1A resource page when you get to part d) first write down an estimate, then come and obtain 8.2.1B resource page....You will need to use the little flags from 8.2.1A in order to help you solve the problem 8­62 see if you can see the generalization 8­63 Time to test what you came up with in 8­61 and 8­62. You must do all parts of 8­63, whatever you don't finish in class becomes homework 5 8­62 Generalization of similar figures and the area When working with two similar figures take the scale factor/ratio/zoom factor etc. and square it....then multiply it by the original area to find the area of the new figure EXAMPLES Area of shape = 5 new shape has a zoom factor of 2 5(2)2 = 20 Perimeter = 5 new shape perimeter = 5 * 2 = 10 Area of shape = 7 new shape has a zoom factor of 6 7(6)2 = 252 Perimeter = 7 new shape perimeter = 7 * 6 = 42 6 8­63a) 17(5)2 425 b) NOW we are given the larger shape, so instead of multiplying we divide 656 / (4)2 656 / 16 41 un2 c) The linear scale factor is 3/2 ratio of the areas is (3/2)2 9/4 d) linear scale factor is (1/2)2 so the are of his office is 1/4 what he thought it was, therefore he should only be paying $50 7 What did we learn today? When you are comparing similar figures the perimeter is found by multiplying by whatever the zoom factor is, however the area is found by taking the zoom factor and squaring it and then multiplying. 8 Homework: In Class 8 ­ 61 to 8 ­ 63 Review and Preview 8 ­ 65 to 8 ­70 Plus extra problem 8­74 and Method and meanings Make sure to draw a picture for 8 ­ 66 using similar figures 8 ­ 67 think of triangles and using trig to find the area you need 9