Similar Shapes Area Demonstration This resource provides animated

Similar Shapes – Area – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

8 cm 4 cm Lengths × 2 2 cm 4 cm = 8 cm 2 Area × 4 = 32 cm 2 The lengths of these shapes have been multiplied. What has happened to their area? Why? 6 cm 2 cm Lengths × 3 2 cm 6 cm = 4 cm 2 Area × 9 = 36 cm 2

Scale Factor = 2 Length × 2 Area × 4 If we multiply the lengths of a shape by a scale factor (SF), the area of the shape is multiplied by that scale factor squared. Scale Factor = 3 Length × 3 Area × 9 Scale Factor = 4 This is because the multiplication happens in 2 dimensions. New Length = original length × SF New Area = original area × SF 2 Length × 4 Area × 16

These pairs of shapes are similar. How can we express the relationships between each pair? 16 cm 8 cm 4 cm 6 cm Scale Factor = 8÷ 4=2 Scale Factor = 16 ÷ 6 = 2. 66… Length Ratio = (simplify) 4: 8 1: 2 Length Ratio = (simplify) 6 : 16 3: 8 Ratios are easier to use to compare lengths, areas and volumes of similar shapes.

These pairs of shapes are similar. Express their… 4 cm length relationship area relationship 6 cm 2 cm 1 cm 3 cm 1 cm = 1 cm 2 = 16 cm 2 Length Ratio = = 2 cm 2 1: 4 Length Ratio = = 18 cm 2 1: 3 squared Area Ratio = 1 : 16 Area Ratio = How is the length ratio related to the area ratio? 2 : 18 1: 9

These pairs of shapes are similar. Express their… length relationship area relationship 8 cm 4 cm 2 cm 6 cm 4 cm 2 cm 3 cm = 8 cm 2 = 32 cm 2 Length Ratio = 2: 4 1 : 2 squared Length Ratio = 8 : 32 1: 4 Area Ratio = = 8 cm 2 = 18 cm 2 2: 3 squared 8 : 18 4: 9 The area ratio of similar shapes is the length ratio squared.

The area ratio of similar shapes is the length ratio squared. Is this also true for surface area? 6 cm 2 cm 6 cm Surface Area = 4 cm 2 × 6 = 24 cm 2 Surface Area = 36 cm 2 × 6 = 216 cm 2 Length Ratio = 2: 6 1: 3 Area Ratio = 24 : 216 (÷ 24) 1: 9

The area ratio of similar shapes is the length ratio squared. Is this also true for surface area? 6 cm 2 cm Surface Area = 4 cm 2 × 6 = 24 cm 2 Surface Area = 36 cm 2 × 6 = 216 cm 2 Length Ratio = 2: 6 1: 3 Area Ratio = 24 : 216 (÷ 24) 1: 9

These are similar shapes. What is the area of the larger shape? 4 cm 1 cm Area = 5 cm 2 Length Ratio = Area Ratio = 1 : 16 1: 4 1 : 16 square How much is one part worth? 5 × 16 = 80 cm 2

These are similar shapes. What is the area of the larger shape? 3 cm 2 cm Area = 12 cm 2 Length Ratio = 2: 3 square Area Ratio = 4: 9 How much is one part worth? (12 ÷ 4) × 9 = 27 cm 2

These are similar shapes. What is the area of the larger shape? 5 cm 3 cm Area = 18 cm 2 Length Ratio = 3: 5 square Area Ratio = 9 : 25 How much is one part worth? (18 ÷ 9) × 25 = 50 cm 2

These are similar shapes. What is the area of the larger shape? 6 cm 4 cm Area = 20 cm 2 Length Ratio = Area Ratio = 4: 9 4: 6 2: 3 4: 9 square How much is one part worth? (20 ÷ 4) × 9 = 45 cm 2

These are similar shapes. What is the area of the larger shape? 6 cm 4 cm YOUR TURN These are similar shapes. What is the area of the larger shape? 1 cm Area = 8 cm 2 5 cm Area = 20 cm 2 Length Ratio = Area Ratio = 4: 9 4: 6 2: 3 4: 9 square How much is one part worth? (20 ÷ 4) × 9 = 45 cm 2 Length Ratio = 1: 5 Area Ratio = 1 : 25 square How much is one part worth? 8 × 25 = 200 cm 2

These are similar shapes. What is the area of the larger shape? 3 cm 6 cm 4 cm YOUR TURN These are similar shapes. What is the area of the larger shape? 9 cm Area = 6 cm 2 Area = 20 cm 2 Length Ratio = Area Ratio = 4: 9 4: 6 2: 3 4: 9 Length Ratio = square How much is one part worth? (20 ÷ 4) × 9 = 45 cm 2 Area Ratio = 1: 9 3: 9 1: 3 1: 9 square How much is one part worth? 6 × 9 = 54 cm 2

These are similar shapes. What is the area of the smaller shape? 1 cm 2 cm Area = 8 cm 2 Length Ratio = 1: 2 square Area Ratio = 1: 4 How much is one part worth? (8 ÷ 4) × 1 = 2 cm 2

These are similar shapes. What is the area of the smaller shape? 5 cm 2 cm Area = 10 cm 2 Length Ratio = 2: 5 square Area Ratio = 4 : 25 How much is one part worth? (10 ÷ 25) × 4 = 1. 6 cm 2

These are similar shapes. What is the area of the smaller shape? YOUR TURN These are similar shapes. What is the area of the smaller shape? 5 cm 2 cm Area = 10 Length Ratio = 7 cm Area = 22 cm 2 2: 5 Length Ratio = 2: 7 square Area Ratio = 4 : 25 How much is one part worth? (10 ÷ 25) × 4 = 1. 6 cm 2 square Area Ratio = 4 : 49 How much is one part worth? (22 ÷ 49) × 4 = 1. 8 cm 2

These are similar shapes. What is the area of the smaller shape? YOUR TURN These are similar shapes. What is the surface area of the smaller shape? 5 cm 2 cm 8 cm Area = 10 Length Ratio = 12 cm 7 cm cm 2 Surface Area = 60 cm 2 2: 5 Length Ratio = square Area Ratio = 4 : 25 How much is one part worth? (10 ÷ 25) × 4 = 1. 6 cm 2 Area Ratio = 4: 9 8 : 12 2: 3 4: 9 square How much is one part worth? (60 ÷ 9) × 4 = 26. 7 cm 2

4 cm Area = 1 cm 2 Area = 9 cm 2 Length Ratio = Area Ratio = 1: 3 1: 9 square root How much is one part worth? (4 ÷ 3) × 1 = 1. 3 cm

20 cm Surface Area = 9 cm 2 Surface Area = 16 cm 2 Length Ratio = Area Ratio = 3: 4 9 : 16 square root How much is one part worth? (20 ÷ 4) × 3 = 15 cm

YOUR TURN 20 cm Surface Area = 9 cm 2 Surface Area = 16 cm 2 Length Ratio = Area Ratio = 3: 4 16 cm 3: 4 9 : 16 Area = 16 cm 2 Area = 100 cm 2 Length Ratio = square root How much is one part worth? (20 ÷ 4) × 3 = 15 cm Area Ratio = 2: 5 4 : 10 2: 5 16 : 100 square root How much is one part worth? (16 ÷ 5) × 2 = 6. 4 cm

YOUR TURN 2 cm 20 cm Surface Area = 9 cm 2 Surface Area = 16 cm 2 Length Ratio = Area Ratio = 3: 4 9 : 16 Surface Area = 4 cm 2 Surface Area = 64 cm 2 Length Ratio = square root How much is one part worth? (20 ÷ 4) × 3 = 15 cm Area Ratio = 1: 4 2: 8 1: 4 4 : 64 square root How much is one part worth? 2 : �� (2 ÷ 1) × 4 = 8 cm

① ② These are pairs of similar shapes. Find the length ratio and area ratio for each pair. 15 cm 2 cm 8 cm Length Ratio = 1: 4 Area Ratio = 1: 16 6 cm Length Ratio = 2: 5 Area Ratio = 4: 25 ③ ④ 16 cm 2 25 cm 2 Length Ratio = 4: 5 Area Ratio = 16: 25 16 cm 2 81 cm 2 Length Ratio = 2: 3 Area Ratio = 4: 9

① ② 5 cm 2 cm Area = 8 cm 2 Area = 80 cm 2 Length Ratio = 2: 5 Area Ratio = 4: 25 Length Ratio = 3: 8 Area Ratio = 9: 64 ③ Surface Area = 32 cm 2 12 cm Area = 9 cm 2 16 cm Area = 25 cm 2 Length Ratio = 3: 5 Area Ratio = 9: 25 15 cm Length Ratio = 2: 3 Area Ratio = 16: 36 ④ Surface Area = 72 cm 2

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