10.solutionoftriangles
5
SOLUTION OF TRIANGLES PAPER 2 1. Diagram 1 shows a quadrilateral ABCD such that ABC is acute. 40.5 9.5 cm 12.3 cm 5.2 cm 9.8 cm D C B A DIAGRAM 1 (a) Calculate (i) ABC (ii) ADC (iii) the area , in cm , of quadrilateral ABCD. [8 marks] (b) A triangle has the same measurements as those given for triangle ABC, i.e., =12.3 cm, = 9.5 cm, dan = 40.5 , but which is different in shape to triangle ABC . (i) Sketch the triangle , (ii) State the size of [2 marks] 2. Diagram 2 shows a triangle ABC. 15 cm 65 20 cm C B A DIAGRAM 2 1
-
Upload
mk-joey-tham -
Category
Documents
-
view
214 -
download
1
description
addmath
Transcript of 10.solutionoftriangles
SOLUTION OF TRIANGLES
PAPER 2
1. Diagram 1 shows a quadrilateral ABCD such that ABC is acute.
40.5
9.5 cm
12.3 cm
5.2 cm
9.8 cm
D
C
B
A
DIAGRAM 1
(a) Calculate (i) ABC(ii) ADC(iii) the area , in cm , of quadrilateral ABCD. [8 marks]
(b) A triangle has the same measurements as those given for triangle ABC, i.e., =12.3 cm, = 9.5 cm, dan = 40.5 , but which is different in shape
to triangle ABC .(i) Sketch the triangle ,(ii) State the size of [2 marks]
2. Diagram 2 shows a triangle ABC.
15 cm
65
20 cm
C
B
A
DIAGRAM 2
(a) Calculate the length of AC. [2 marks]
(b) A quadrilateral ABCD is now formed so that AC is the diagonal, ACD = 40 and AD = 16 cm.
1
Calculate the two possible values of ADC. [2 marks]
(c) Using the acute ADC in (b), calculate (i) the length of CD(ii) the area of the quadrilateral ABCD . [6 marks]
3.
48 50
7.0 cm
5.5 cm
S
R
QP
DIAGRAM 3
Diagram 3 shows SPR and QPR where PR = 5.5 cm, SP = 7.0 cm, RPQ = 50 and RQP = 48 . Given that the area of PQR is twice the area of PSR, calculate
(a) the length of PQ [3 marks]
(b) the area of PSR [3 marks]
(c) the length of SR [4 marks]
4. In diagram 4 , AB= 13 cm , BC= 7 cm , AG = 6 cm , GE = 24 cm, FE = x cm , and . Calculate
2
(a) the length of CE, [3 marks]
(b) CEA , [3 marks]
(c) the value of x if the area of is equal to the area of . [4 marks]
G FE
D
C
B
A
24 cm
x cm6 cm
7 cm
13 cm
DIAGRAM 4
5. Diagram 5 shows a quadrilateral ABCD.
9 cm
6 cm
5 cmD
C
B
A
DIAGRAM 5
The area of triangle BCD is 13 and is acute. Calculate
(a) [2 marks](b) the length , in cm , of BD, [2 marks]
(c) [3 marks](d) the area , in cm , of quadrilateral ABCD . [3 marks]
ANSWER – SOLUTIONS OF TRIANGLES
3
1. (a) (i) 57.23 or 57
(ii) 106 4
(iii) 82.38 cm
(b) (i)
BA'B'
C'
(ii) 122.77 or 122
2. (a) 19.27 cm
(b) 50 or , 129.27 or 129 16
(c) (i) 24.89 cm
(ii) 290.1 cm
3. (a) 7.329 cm
(b) 7.720 cm
(c) 2.952 cm
4. (a) 26.46 cm
(b)
(c) x = 8.832
5. (a)
(b) 5.574 cm
(c)
(d) 35.44 cm
4
