Mixed geometry questions
(angle facts, area of a triangle, Pythagoras’ theorem, trigonometry, sine rule and cosine rule, similarity)
1.
X 3 .2 c m Y
D ia g ram N O T
a c cu rately d raw n
1 .7 cm
XY = 3.2 cm.
XZ = 1.7 cm.
Calculate the length of YZ.
Give your answer correct to 3 significant figures.
…………………………. cm
(Total 3 marks)
2.
Diagram NOT
accurately drawn
AC = 12 cm.
Angle ABC = 90°.
Angle ACB = 32°.
Calculate the length of AB.
Give your answer correct to 3 significant figures.
................................. cm
(Total 3 marks)
1
D iag ram N O T D iagram N O T
a ccu rately dra waccu
n rately draw n
3.
A A B B C C
48° 48° 30° 30 °
D D E x E x
y F y F
Diagram NOT
accurately drawn
G G
BEG and CFG are straight lines.
ABC is parallel to DEF.
Angle ABE = 48°.
Angle BCF = 30°.
(a) (i) Write down the size of the angle marked x.
x = ...................
(ii) Give a reason for your answer.
...........................................................................................................................
(2)
(b) (i) Write down the size of the angle marked y.
y = ...................
(ii) Give a reason for your answer.
...........................................................................................................................
(2)
(Total 4 marks)
2
4.
BE is parallel to CD.
AB = 9 cm, BC = 3 cm, CD = 7 cm, AE = 6 cm.
(a) Calculate the length of BE.
………………… cm
(2)
(b) Calculate the length of DE.
………………… cm
(2)
(Total 4 marks)
3
5.
A
D iag ram N O T
acc u rate ly d ra w n
38°
B C
8 .5 c m
BC = 8.5 cm.
Angle ABC = 90°.
Angle ACB = 38°.
Work out the length of AC.
Give your answer correct to 3 significant figures.
......................... cm
(Total 3 marks)
6.
C
D iag ra m N O T
ac c u rate ly d ra w n
73°
1 0 cm
7 cm
A B
AC = 7 cm,
BC = 10 cm,
Angle ACB = 73°.
Calculate the length of AB.
Give your answer correct to 3 significant figures.
……………………. cm
(Total 3 marks)
4
7.
C Diagram NOT
accurately drawn
5 .4 cm
A 2 .3 cm B
AB = 2.3 cm.
BC = 5.4 cm.
Angle BAC = 90°.
Work out the size of angle ABC.
Give your answer correct to 3 significant figures.
.....................................
(Total 3 marks)
8.
A
Diagram NOT
accurately drawn
10 m
12 m
C
15 m
B
AB = 12 m.
AC = 10 m.
BC = 15 m.
Calculate the size of angle BAC.
Give your answer correct to one decimal place.
................................°
(Total 3 marks)
5
9. The diagram represents a vertical flagpole, AB.
The flagpole is supported by two ropes, BC and BD, fixed to the horizontal ground at C and at D.
D iag ram N O T
accu rately draw n
1 2 .8 m
42°
C A D
6 .8 m
AB = 12.8 m.
AC = 6.8 m.
Angle BDA = 42.
(a) Calculate the length of rope BC.
Give your answer correct to 3 significant figures.
………………………… m
(3)
(b) Calculate the length of the rope BD.
Give your answer correct to 3 significant figures.
………………………… m
(3)
(c) Calculate the size of angle BCA.
Give your answer correct to 3 significant figures.
…………………………
(3)
(Total 9 marks)
6
10.
Diagram NOT
accurately drawn
ABC is a straight line and BD = CD.
(a) Work out the size of angle x.
....................................º
(2)
(b) Work out the size of angle y.
....................................º
(3)
(Total 5 marks)
11.
1 2 .5 cm Diagram NOT
A accurately drawn
15 cm
6 cm
P
B
Y
AB is parallel to XY.
The lines AY and BX intersect at P.
AB = 6 cm.
XP = 12.5 cm.
XY = 15 cm.
Work out the length of BP.
............................ cm
(Total 3 marks)
7
12.
A
Diagram NOT
accurately drawn
6 .8 cm
B C
9 .5 cm
Work out the area of triangle ABC.
2
………………. cm
(Total 2 marks)
13.
Diagram NOT
accurately drawn
AB = 8 cm, BC = 14 cm
Angle ABC = 106
Calculate the area of the triangle.
Give your answer correct to 3 significant figures.
2
………………..cm
(Total 3 marks)
14.
A
Diagram NOT
accurately drawn
7 cm
B C
8 cm
AB = 7 cm, BC = 8 cm.
Work out the area of the triangle.
2
............................ cm
(Total 2 marks)
8
15.
A B
Diagram NOT
accurately drawn
1 2 .6 cm 4 .7 cm
AC = 12.6 cm.
BC = 4.7 cm.
Angle ABC = 90°.
Calculate the length of AB.
Give your answer correct to 3 significant figures.
………………….. cm
(Total 3 marks)
16.
A
Diagram NOT
8 cm accurately drawn
B 70º C
15 cm
AC = 8 cm,
BC =15 cm,
Angle ACB = 70°.
(a) Calculate the length of AB.
Give your answer correct to 3 significant figures.
................................ cm
(3)
(b) Calculate the size of angle BAC.
Give your answer correct to 1 decimal place.
...................................°
(2)
(Total 5 marks)
9
17.
A 2 .1 m D
Diagram NOT
accurately drawn
3 .2 m
1 .9 m
B C
ABCD is a trapezium.
AD is parallel to BC.
Angle A = angle B = 90.
AD = 2.1 m,
AB = 1.9 m,
CD = 3.2 m.
Work out the length of BC.
Give your answer correct to one decimal place.
………………………… m
(Total 4 marks)
18.
A 5 .8 c m D
Diagram NOT
4 .3 c m accurately drawn
50º
B C
ABCD is a trapezium.
AD is parallel to BC.
Angle C = angle D = 90°.
Angle B = 50°.
AD = 5.8 cm.
AB = 4.3 cm.
Calculate the length of BC.
Give your answer correct to one decimal place.
............................... cm
10
(Total 4 marks)
11
