Find the ratio of the areas of the two triangles in simplest form. AΞπ΄π΅πΆ = AΞABD AΞπ΄π΅πΆ = AΞAπ·πΆ 11-7: Ratios of Areas Formulas so farβ¦ β’ π¨ππππππ = ππ ο π¨πππππππππ = ο π¨πππππππ = π β π β π ο πͺππππππ: β¦ π¨ = π ππ β¦ πͺ = ππ π β’ π¨πππππππππ = π β π β’ π¨πππππππππππππ = π β π β’ π¨ππππππππ = π π π β’ π¨πππππππ = π π π π βπ β π π π π ππ + ππ β π π π β¦ π¨ππππππ = π½ πππ β π ππ β¦ π³πππππ ππ π¨π© = π½ πππ β ππ π 11-7 Objectives β’ Find the ratio of areas of two triangles. β’ Understand and apply the relationships between scale factors, perimeters, and areas of similar figures. As we observed in the warm upβ¦ 1. If two triangles have equal heights, then the ratio of their areas equals the ratio of their bases. 2. If two triangles have equal bases, then the ratio of their areas equals the ratio of their heights. 3. What about similar triangles? β¦ Find the ratios of the areas of the similar triangles and make a conjecture. 3 8 8 8 Is this true for any two similar shapes? 3 3 Yes. Yes it is. : If the scale factor of two similar figures is π: π, then: 1. The ratio of the perimeters is π: π. 2. The ratio of the areas is π2 : π 2 (Recall, scale factor is the ratio of two corresponding side lengths of similar polygons.) Find the ratio of perimeters and areas of the similar figures. Find the ratio of perimeters and areas of the similar figures. Ξπ΄π·πΆ: π₯πΆπ·π΅ A pentagon with sides 3 π, 4 π, 4 π, 6 π, and 7 π has area 48 π2. Find the perimeter of a similar pentagon whose area is 27 π2. p. 458 (bottom of page): #1-11 odd, 15, 17, 10, 16
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