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Triangle and Quadrilateral Solutions

This document contains solutions to 5 problems involving triangles and quadrilaterals. Problem 1 involves calculating angles and areas of a quadrilateral given angle and side measurements. Problem 2 involves calculating side lengths and areas using the Law of Sines and Cosines. Problem 3 calculates side lengths and areas of two triangles where one area is twice the other. Problems 4 and 5 similarly use trigonometry and given information to solve for unknown side lengths, angles, and areas.

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Mohana Roman
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429 views5 pages

Triangle and Quadrilateral Solutions

This document contains solutions to 5 problems involving triangles and quadrilaterals. Problem 1 involves calculating angles and areas of a quadrilateral given angle and side measurements. Problem 2 involves calculating side lengths and areas using the Law of Sines and Cosines. Problem 3 calculates side lengths and areas of two triangles where one area is twice the other. Problems 4 and 5 similarly use trigonometry and given information to solve for unknown side lengths, angles, and areas.

Uploaded by

Mohana Roman
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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SOLUTION OF TRIANGLES

PAPER 2

1. Diagram 1 shows a quadrilateral ABCD such that  ABC is acute.

D 5.2 cm
C
9.8 cm 12.3 cm

9.5 cm
40.5
A

DIAGRAM 1

(a) Calculate
(i)  ABC
(ii)  ADC
(iii) the area , in cm 2 , of quadrilateral ABCD. [8 marks]

(b) A triangle A' B 'C ' has the same measurements as those given for triangle ABC,
i.e., A'C ' =12.3 cm, C ' B ' = 9.5 cm, dan  B ' A'C ' = 40.5  , but which is
different in shape to triangle ABC .
(i) Sketch the triangle A' B 'C ' ,
(ii) State the size of  A' B 'C ' [2
marks]

2. Diagram 2 shows a triangle ABC.


A

20 cm

65
B

15 cm

DIAGRAM 2

(a) Calculate the length of AC. [2 marks]

1
(b) A quadrilateral ABCD is now formed so that AC is the diagonal,  ACD = 40 
and AD = 16 cm.
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.
S

R
7.0 cm

5.5 cm

50  48 
Q
P

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]

2
4. In diagram 4 , AB= 13 cm , BC= 7 cm , AG = 6 cm , GE = 24 cm, FE = x cm ,
BAG  60o and DFE  90o . Calculate

(a) the length of CE, [3 marks]

(b)  CEA , [3
marks]

(c) the value of x if the area of DFE is equal to the area of BAG . [4 marks]
C

7 cm

B D

13 cm

60o
A E
6 cm G F x cm

24 cm

DIAGRAM 4

5. Diagram 5 shows a quadrilateral ABCD.

D
5 cm
C
40o

6 cm

B
9 cm
A

DIAGRAM 5

The area of triangle BCD is 13 cm2 and BCD is acute.


Calculate

(a) BCD, [2 marks]


(b) the length , in cm , of BD, [2 marks]
(c) ABD, [3 marks]
(d) the area , in cm 2 , of quadrilateral ABCD . [3 marks]

3
ANSWER – SOLUTIONS OF TRIANGLES

1. (a) (i) 57.23  or 57 14'


(ii) 106  4 '
(iii) 82.38 cm 2

(b) (i)
C'

A' B' B

(ii) 122.77  or 122  46 '

2. (a) 19.27 cm
(b) 50  73' or 50 44' , 129.27  or 129  16 '
(c) (i) 24.89 cm
(ii) 290.1 cm 2

3. (a) 7.329 cm
(b) 7.720 cm 2
(c) 2.952 cm

4. (a) 26.46 cm
(b) 40.89o or 40o53'
(c) x = 8.832

5. (a) 60o 4'


(b) 5.574 cm
(c) 116o 32'

4
(d) 35.44 cm 2

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