Module 3: Spaces in the Environment
MODULE 3 UNIT 2 Shapes
Answers
2.1 Common 2-D and 3-D Shapes
1.
Rhombus or square or rectangle
2.
Regular hexagon
3.
3 cm
60˚
4.
4 cm
Yes: rhombus
5.
Yes: rectangle
6.
Square, rectangle, rhombus, parallelogram, kite
7.
Trapezium, quadrilateral
2.2 Angle Properties of Polygons
1.
(a)
2.
(a) Exterior = 45 ° ,
Interior = 135 °
(b) Exterior = 36 ° ,
Interior = 144 °
30 °
(b)
(c)
5°
3.
(a)
150 °
(b) 1800 °
4.
(a)
162 °
(b)
5.
72 °
6.
30 sides
7.
(d)
18 °
6°
3240 °
(a)
(i) 12
(ii)
(b)
Interior angle = 123 ° , Exterior angle = 57 °
No. of sides =
8.
See next page
9.
(a) 90
10.
(a)
(b)
72
(iii)
20
(iv)
60
360
which is not an exact integer, so a regular polygon not possible.
57
(90 − 2) × 180 = 15840 °
360 °
no. of sides
(b)
Interior angle = 180 ° − exterior angle
= 180 ° −
(c)
CCSLC
360 °
n
sum = 180 ° (n − 2)
1
CXC
Module 3: Spaces in the Environment
MODULE 3 UNIT 2 Shapes
Answers
2.2
8.
(a)
Number
of Sides
Exterior
Angles
Interior
Angles
Sum of Interior
Angles
4
90 °
90 °
360 °
5
72 °
108 °
540 °
6
60 °
120 °
720 °
7
51 37 °
128 47 °
900 °
8
45 °
135 °
1080 °
9
40 °
140 °
1260 °
10
36 °
144 °
1440 °
12
30 °
150 °
1800 °
(b)
If n = no. of sides of regular polygon, sum = (n − 2) × 180 ° .
(c)
Sum of interior angles.
2.3 Quadrilaterals
1.
Rectangle, Square
2.
(a) Rectangle (but not square), Rhombus (but not square)
(b)
3.
4.
Rectangle, Rhombus, Parallelogram
(a) Kite and Isosceles Trapezium
(b)
CCSLC
2
CXC
Module 3: Spaces in the Environment
MODULE 3 UNIT 2 Shapes
Answers
2.3
5.
(a) Trapezium
(d) Rhombus
(b) Kite
(e) Trapezium
(c) Rectangle
(f) Parallelogram
6.
Parallelogram (unless it is a rectangle), Rhombus (unless it is a square),
Kite, Trapezium (unless it is isosceles)
7.
(a) The quadrilateral must be a rhombus.
(b) The quadrilateral could be a square if it contains 4 right angles.
8.
(a) Rectangle, Square, Rhombus
(b)
(c)
9.
CCSLC
Name
Order of Rotational Symmetry
Rectangle
2
Square
4
Parallelogram
2
Rhombus
2
A Square
B Rectangle
C Rhombus
E Trapezium
F Kite
G General quadrilateral
3
D Parallelogram
CXC
Module 3: Spaces in the Environment
MODULE 3 UNIT 2 Shapes
Answers
2.3
10. A variety of acceptable solutions, e.g.
START
ARE THE
SIDES OF
EQUAL
LENGTH
?
NO
YES
ARE
ALL THE
DIAGONALS
THE SAME
LENGTH
?
YES
ARE
THERE
4
RIGHT
ANGLES
?
NO
ARE
THERE
2 PAIRS OF
PARALLEL
SIDES
?
YES
NO
YES
ARE
OPPOSITE
ANGLES
EQUAL
?
YES
NO
ARE
THERE
2
PARALLEL
SIDES
?
NO
YES
NO
Kite
CCSLC
Square
Rhombus
Rectangle
Parallelogram
4
Trapezium
Other
CXC