Grade B Scale Factors and Similarity Use scale

Grade B Scale Factors and Similarity Use scale factors as a link to similarity.

Key Vocabulary Similarity Scale Factor Linear Scale Factor Area Scale Factor Volume Scale Factor Length Height Parallel

How to solve problems involving scale factors and similarity These two triangles are similar. Find all the missing lengths. 3 cm 6 cm 5 cm 4 cm 10 cm 8 cm Step 1) Find the scale factor by looking at how you can go from 4 cm to 8 cm. In this case we multiplied by 2. Linear Scale Factor = 2 Step 2) Multiply all the sides on the original shape to give you the sides on the other shape. 3 × 2 = 6 cm 5 × 2 = 10 cm

How to solve problems involving scale factors and similarity These two rectangles are similar. Find the missing length x. 6 cm A B 2 cm x cm 15 cm Step 1) Find the scale factor by looking at how you can go from 6 cm to 2 cm. In this case we divide by 3. Linear Scale Factor = 3 Step 2) Divide all the sides on shape A to give you the sides on shape B. 15 ÷ 3 = 5 cm Therefore x = 5 Remember: To find lengths of the smaller shape, we need to divide!

How to solve problems involving area scale factors These two shapes are similar. Find the area of shape B. B A Remember: ASF = LSF 2 Area = 40 cm 2 4 cm 8 cm Step 1) Find the linear scale factor by looking at how you can go from 8 cm to 4 cm. In this case we divide by 2. Linear Scale Factor = 2 Step 2) Area Scale Factor = Linear Scale Factor 2 Therefore ASF = 22 = 4 Step 3) Area of A multiplied by 4 will give us the area of shape B 40 × 22 = 160 cm 2

How to solve problems involving volume scale factors These two shapes are similar. Find the missing area x. B Volume = 120 ml A 16 cm Remember: VSF = LSF 3 8 cm Step 1) Find the linear scale factor by looking at how you can go from 16 cm to 8 cm. In this case we divide by 2. Linear Scale Factor = 2 Step 2) Volume Scale Factor = Linear Scale Factor 3 Therefore VSF = 23 = 8 Step 3) Volume of A multiplied by 8 will give us the area of shape B 120 × 23 = 960 ml 3

Solve the following problems – now you try. . . 1. Find the missing length. x 3 cm 2 cm 12 cm 8 cm 2. Find the missing area. Area = 12 cm 2 9 cm 3. Find the missing volume. 108 cm 2 Volume = 800 ml 3 10 cm 51. 2 ml 3 4 cm

Problem Solving and Reasoning LSF = 9 ÷ 1. 5 = 6 AD 2 × 6 = 12 BD 12 – 2 = 10

Problem Solving and Reasoning now you try. . . LSF = 1. 5 AB 4 × 1. 5 = 6 BD 6 – 4 = 2

Reason and explain The length of BC is 24 cm The length of GH is 11. 25 cm Angles of the larger shape will be bigger because the shape has been enlarged.