1819 C2X §4.4

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

Which exercises/theories should I discuss on the board?

Calculating unknown sides in similar figures

When calculating unknown sides in similar figures, you can use the scale factor (see LessonUp §4.2).

To make it easier to find out which sides are corresponding sides, you should sketch both figures in the same position.

Example

Triangle ABC and triangle PQR are similar figures. Calculate the length of AC and PR.

Sketch

Calculations

Scale factor and area

Rectangles B, C and D are

enlargements of rectangle A.

The scale factors are:

B: 2

C: 3

D: 4

Scale factor and area

Perimeter rectangle A = 2 + 1 + 2 + 1 = 6 cm

Perimeter rectangle B = 4 + 2 + 4 + 2 = 12 cm

Perimeter rectangle C = 6 + 3 + 6 + 3 = 18 cm

Perimeter rectangle D = 8 + 4 + 8 + 4 = 24 cm

12 = 6 x 2; 18 = 6 x 3; 24 = 6 x 4.

The perimeter is multiplied by the scale factor.

Scale factor and area

The area is multiplied by the scale factor squared!

Scale factor and area

When the dimensions (length/width/height) of a figure are multiplied by a factor s, the perimeter is also multiplied by s, but the area is multiplied by      .

(When you learn about volume you will find that the volume is multiplied by      )

s​2​​

s​3​​

Homework Tuesday

• Make §4.4:

Support: 24, 25, S26, 27, S28, 28, 29

Standard: 24, 25, 26, 27, 28, 29, 30

Challenge: 24, 26, 27, 28, 29, 30, C5

• Correct your answers with a red pen