2.2 Classifying and constructing triangles

8. Calculate the area of each square.

9. What can you deduce from this exercise?

10. Deduction: Write out Pythagoras’ theorem in the space below by making use of the triangle that is provided.

11. Solve x in each of the following triangles:(You may make use of your calculator.)

1.4

12. Do the calculations to determine whether the following is a right-angled triangle or not:

12.1 $\Delta$ DEF with DE = 8 cm, EF = 10 cm, DF = 6 cm

13. AREA OF TRIANGLES

13.1 Construct rectangle ABCD with AB = 45 mm and AD = 25 mm on a sheet of paper and cut it out. Draw diagonal AC .

13.2 Calculate the area of rectangle ABCD .

13.3 Cut out $\Delta$ ABC . What is the area of $\Delta$ ABC ?Paste it here.

• Area of $\Delta$ ABC = ................. mm²

13.4 Are you able to develop a formula for determining the area any triangle?

Write it here:

13.5 Calculate the area of $\Delta$ ABC .

13.6 In the figure SQ = 15 cm, QR = 7 cm and PR = 9 cm.

Important : Provide all necessary information on your sketch. Check to see what you may need to complete the instructions fully.

(a) Calculate the area of $\Delta$ PSQ (accurate to 2 decimals).

(b) Now calculate the area of $\Delta$ PSR . Suggestion : You will first have to calculate the area of another triangle.

13.7 Calculate the area of ABCD .

14.1

14.3

15. Playing in a park is a necessary aspect of the development of a child.

• You have been asked to supply slides. The problem that is involved requires calculating the length of the poles that are needed. Make use of the knowledge that you have accumulated to supply a plan to erect the slides.

The following is required:

15.1 a sketch

15.2 a scale, e.g. 1 cm = 1 m

15.3 Calculations must be completed fully.

Assessment

Memorandum

ACTIVITY 1

1.1 a) all 3 Acute-angled

b) one 90 ^o angled

c) one obtuse-angled

1.2 a) 2 even sides

b) 3 even sides

c) sides differ in length

2. The sum of the interior angles of any triangle is 180º

ACTIVITY 2

10. r ² = p ² + q ²

• x ² = 12 ² + 5 ²

= 144 + 25

= 169

$\therefore$ x = 13

• 20 ² = 8 ² + x ²

x ² = 400 – 64

= 336

$\therefore$ x $$ 18,3 cm

11.3 $\nabla$ ABC : x ² = 70 ² – 29 ²

= 4 900 – 841

= 4 059

$\therefore$ x $$ 63,7 mm

11.4 y ² = 4 ² + 3 ²

= 16 + 9

= 25

$\therefore$ x $$ 9,4cm

12. DE ² + DF ² = 100 = EF ²

$\therefore$ DEF right angled

(Pythagoras)

• ½ x b x h
• BC ² = 13 ² – 5 ²

= 169 – 25

= 144

$\therefore$ BC = 12 cm

Area ABC = ½ x b x h

= ½ x 12 x 5

= 30cm ²

13.6 (a) PS ² = 9 ² – 8 ²

= 81 – 64

= 17

$\therefore$ PS = 4,12 cm

Area PSQ = ½ x b x h

= ½ x 15 x 4,12

= 30,9cm ²

13.6 ( b ) Area PSR = ½ x 8 x 4,12

= 16,4 cm ²

Area PRQ = area PSQ – PSR

= 30,9 – 16,4

= 14,5 cm ²

13.7 AC ² = 12 ² + 8 ²

= 208

$\therefore$ AC $$ 14,4

AD ² = 16 ² – 14,4 ²

= 256 – 207,36

= 48,64

$\therefore$ AD = 6,97

Area ABCD = area ABC + area ACD

= (½ x 12 x 8) + (6,97 x 14,4 x ½)

= 48 + 50,18

= 98,18 square units

• a ² = 8 ² – 7 ²

= 15

$\therefore$ a $$ 3,9

b ² = (3,9) ² + 4 ²

= 15,21 + 16

= 31,21

$\therefore$ b $$ 5,6

• x = 18 (radius)

y ² = 36 ² – 13 ²

= 1 296 – 169

= 1 127

$\therefore$ y = 33,6

• UV ² = 12 ² – 7 ²

= 95

$\therefore$ UV = 9,8

VS ² = 14 ² + ( $$ 9,8) ²

= 196 + 95

= 291

$\therefore$ VS = 17,1

y ² = ( $$ 17,1) ² + 5 ²

= 291 + 25

= 316

$\therefore$ y = 17,8