1. Area & Volume Scale Factor
Similar Triangles
Area & Volume Scale Factor

2. MENU
Recap
AREA
VOLUME

3. Similar shapes Are Enlargements of each other
Corresponding angles are equal
Sides are related by the same scale factor

4. Similar Triangles Triangles are similar if matching
angles remain the same size.
100º
30º
50º
100º
30º
50º

5. To calculate a length x 3 x 3 15 5 1 3 5 4 6 15 12 18 Scale factor 3

6. Harder example C A E D B 3 4 6
Triangle ABC is similar to triangle ADE.
DE is parallel to BC.
Calculate the length of BC

7. Harder example A E D 3 4 9 6 12 C B 9 3
x 3

8. …and then… AB & DE are parallel Explain why ABC is similar to CDE 5
<CED = <BAC Alternate Angles A B
<EDC = <ABC Alternate Angles
<ECD = <ACB Vert Opp Angles 3 C 6 D E ?
Triangle ABC is similar to Triangle CDE

9. …and then… Calculate the length of DE AC corresponds to CE
Scale Factor = 2 5 A B
AB corresponds to DE
DE = 2 x AB 3 C
DE = 10cm 6 D E ?

10. Summary – Similar shapes
To calculate missing sides, we first of all need the scale factor
We then either multiply or divide by the scale factor
To show that 2 shapes are similar we can either show that all of the sides are connected by the scale factor or show that matching angles are the same

11. AREA SCALE FACTOR AREA SCALE FACTOR = 4 40cm² 10cm² 2cm 5cm
ENLARGE rectangle
Scale Factor 2
40cm²
4 cm
10 cm
AREA SCALE FACTOR = 4

12. AREA SCALE FACTOR AREA SCALE FACTOR = 9 90cm² 10cm² 2cm 5cm
ENLARGE rectangle
Scale Factor 3
90cm²
6 cm
15 cm
AREA SCALE FACTOR = 9

13. ASF = LSF² AREA SCALE FACTORS 2 4 3 9 Reflect the Length Scale Factor2² 3²
AREA SCALE FACTOR = LENGTH SCALE FACTOR SQUARED
ASF = LSF²

14. Example Questions - AREA
Calculate the unknown areas Q1 Q2
5 cm
10 cm²
40 cm²
4 cm
12 cm²
8 cm Q3
15 cm
9 cm²
4 cm²
108 cm²
2 cm
3 cm

15. Example Questions - SIDES
Calculate the unknown lengths Q1 Q2
3 cm
10 cm²
250 cm²
2 cm
12 cm² y
10 cm Q3
6 cm x
18 cm²
8 cm²
48 cm²
2 cm
3 cm z

16. VOLUME SCALE FACTOR VOLUME SCALE FACTOR = 27 = 3³ 162 cm³ 1 cm 3 cm
ENLARGE cuboid
Scale Factor 3
6 cm
9 cm
VOLUME SCALE FACTOR = 27
= 3³

17. VSF = LSF³ VOLUME SCALE FACTOR 64cm³ Volume Scale Factor = 2³
ENLARGE cylinder
Scale Factor 2
Volume Scale Factor = 2³
VOLUME SCALE FACTOR = LENGTH SCALE FACTOR CUBED
VSF = LSF³

18. Example Questions - VOLUME
5 cm³
2 cm
8 cm³
3 cm
27 cm³
4.5 cm
135 cm³
6 cm Q3
40 cm³
5 cm³
4 cm
2 cm

19. Example Questions - SIDES
5 cm³
2 cm
6 cm³
1.5 cm
384 cm³
4 cm a
6 cm b
40 cm³ Q3
120 cm³
15 cm³
3.6 cm
1.8 cm c