11.5 areas of similar figures ink.notebook. April 18, Page 142 Page Area of Similar Figures. Page 143. Page 144.
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1 11.5 areas of similar figures ink.notebook Page 14 Page Area of Similar Figures Page 143 Page 144 Lesson Objectives Standards Lesson Notes 11.5 Areas of Similar Figures Press the tabs to view details. 1
2 Lesson Objectives Standards Lesson Notes After this lesson, you should be able to successfully use scale factors and ratios to find missing areas and lengths of similar figures. Lesson Objectives Standards Lesson Notes G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. G.MG.1 Use geometric shapes, their measures, and their properties to describe objects. G.MG.3 Apply geometric methods to solve design problems. Press the tabs to view details.
3 3
4 Ratio of Sides = (Ratio of Sides) = Similar Sides a b (~) Perimeters a b Figures Areas a b Scale Factors and Missing Measures in Similar Figures You can use the areas of similar figures to find the scale factor between them or a missing measure. 4
5 5. ΔJKL ~ ΔPQR. The area of ΔJKL is 40 square inches. Find the area of ΔPQR. 10 in 6. For the pair of similar figures, find the area of the shaded figure. Find the scale factor (ratio of their sides): The ratio of their areas is: To find the area of ΔPQR, write a proportion: 1 in in A = 0 in 6 in So the area of ΔPQR is square inches. 7. For the pair of similar figures, find the area of the shaded figure cm 15.5 cm A = 00 cm 5
6 11.5 areas of similar figures ink.notebook 8. If ãabdc is similar to ãfgjh, find the value of x. x 10 m A = 64 m A = 49 m First find the scale factor. Let k be the scale factor between ãabdc and ãfgjh. Use this scale factor to find the value of x. (set up a proportion). 9. For the pair of similar figures, use the given areas to find the scale factor from the unshaded to the shaded figure. Then find x. in A = 54 in x 8 A = 16 in 6
7 11.5 areas of similar figures ink.notebook 10. For the pair of similar 8 ft figures, use the given areas to find the scale factor from the unshaded to the shaded figure. Then find x. x A = 96 ft A = 169 ft On the Worksheet 7
8 HOMEWORK For each pair of similar figures, find the area of the shaded figure Practice WS Areas of Similar Figures For each pair of similar figures, find the area of the shaded figure.. For each pair of similar figures, find the area of the shaded figure. 3. 8
9 For each pair of similar figures, find the area of the shaded figure. 4. For each pair of similar figures, find the area of the shaded figure. 5. For each pair of similar figures, find the area of the shaded figure. 6. For each pair of similar figures, use the given areas to find the scale factor from the unshaded to the shaded figure. Then find x. 7. 9
10 For each pair of similar figures, use the given areas to find the scale factor from the unshaded to the shaded figure. Then find x. 8. For each pair of similar figures, use the given areas to find the scale factor from the unshaded to the shaded figure. Then find x. 9. For each pair of similar figures, use the given areas to find the scale factor from the unshaded to the shaded figure. Then find x. 10. For each pair of similar figures, use the given areas to find the scale factor from the unshaded to the shaded figure. Then find x
11 For each pair of similar figures, use the given areas to find the scale factor from the unshaded to the shaded figure. Then find x SCIENCE PROJECT Matt has two posters for his science project. Each poster is a rectangle. The length of the larger poster is 11 inches. The length of the smaller poster is 6 inches. What is the area of the smaller poster if the larger poster is 93.5 square inches? 14. ARCHERY A target consists of two concentric similar octagons. The outside octagon has a side length of feet and an area of 19.8 square feet. If the inside octagon has a side length of 1.5 feet, what is the area of the inside octagon? 15. The ratio of the sides of two similar figures is 5 : 7 or The ratio of perimeters = The ratio of areas = 11
12 Decide whether you need the perimeter or area then set up a proportion and solve. 16. The scale on a drawing of a house is 1 in = 5 ft. In the drawing, the kitchen has a perimeter of 18 inches and an area of 0 square inches. a) How many feet of a border wall paper are needed? (use P or A ratio) 17. ËABC ~ ËPRT, AC = 15 in, PT = 6 in, and the area of ËPRT = 4 in. Find the area of ËABC. a) 9.6 in b) 60 in c) 66.7 in d) 150 in b) The floor in the kitchen will be covered with tiles that are 1 square foot each. How many tiles (square feet) will be needed? (use P or A ratio) Find each measure. 0. m 5 1. m 7 1
13 Answers: 13
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