Area Scale Factor Learning Objectives: Know what a similar shape is

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Presentation transcript:

Area Scale Factor Learning Objectives: Know what a similar shape is Grade A 23/11/2018 Learning Objectives: Know what a similar shape is Able to calculate the linear scale factor Able to calculate the area of similar shapes using the area scale factor

Area Scale Factor How much bigger is rectangle B compared to rectangle A? 4cm 2cm 1cm 2cm Length  2cm <-> 4cm Area  2cm2 <-> 8cm2 The dimensions are two times as big. This is called the Linear Scale Factor. The area is four times as big. This called the Area Scale Factor.

Area Scale Factor ASF = LSF2 Linear Scale Factor (LSF) – proportional change in the dimensions of a shape Area Scale Factor (ASF) – proportional change in the area of a shape ASF = LSF2

Area Scale Factor The parallelograms below are similar. The area of the smaller parallelogram is 15cm2. Calculate the area of the larger parallelogram. 4cm 12cm

3. Calculate the area of the larger shape Area = 15 x 9 = 135cm2 A = 15cm2 Calculate the LSF LSF = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 12 4 =3 2. Calculate the ASF ASF = 3 2 = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 𝑎𝑟𝑒𝑎 15 3. Calculate the area of the larger shape Area = 15 x 9 = 135cm2 (The area of the larger shape is 9 times bigger than the smaller shape)

LSF = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 12 8 =1.5 ASF = 1.5 2 = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 99 𝑎𝑟𝑒𝑎 8cm 12cm The area of the larger heart shape is 99cm2. Calculate the area of the smaller heart shape. Area = 99cm2 LSF = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 12 8 =1.5 ASF = 1.5 2 = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 99 𝑎𝑟𝑒𝑎 Area = 99 ÷ 1.5 2 = 44cm2 (The area of the larger shape is 2.25 times bigger than the smaller shape)

The area of the small crescent is 12cm2 The area of the small crescent is 12cm2. Calculate the area of the larger crescent. 8cm 10cm LSF = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 10 8 =1.25 ASF = 1.25 2 = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 𝑎𝑟𝑒𝑎 12 Area = 12 x 1.25 2 = 18.75cm2 The area of the large trapezium is 1521cm2. Calculate the area of the smaller trapezium. 2cm LSF = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 13 2 =6.5 ASF = 6.5 2 = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 1521 𝑎𝑟𝑒𝑎 Area = 1521 ÷ 6.5 2 = 36cm2 13cm

ASF = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 300 12 =25 LSF = 25 =5 Length = 4 x 5 = 20cm 4cm These two regular hexagons are similar. Calculate the length of one of the sides of the larger hexagon. CV CV Area = 12cm2 Area = 300cm2 ASF = 𝐵𝑖𝑔 𝑆𝑚𝑎𝑙𝑙 = 300 12 =25 LSF = 25 =5 Length = 4 x 5 = 20cm