POLYHEDRAL
For Grade VIII/ Semester 2
Written by:
Ririn Aprianita, S.Pd.Si
Standard of Competence
Understanding the properties of cube, cuboid,
prism, pyramid, and their parts, and determining
the measurements.
Basic Competency
Identifying the properties of cube, cuboid, prism,
pyramid, and their parts
Have you ever seen the objects below?
Let’s learn about them
CUBE
CUBE is enclosed by 6 planes
which are the CONGRUENT SQUARES.
The intersecting planes are perpendicular to each other.
G
H
E
F
D
face
C
B
A
CUBE
edge
vertex
How many vertices does the cube have?
8
They are vertex A, B, C, D, E, F, G
How many edges does the cube have? 12
They are edge AB, BC, CD, AD, …,…,…,…,…,…,…,…
6
How many faces does the cube have?
They are face ABCD, EFGH, ADHE, …,…,…
CUBE
BG is called face diagonal (=diagonal sisi).
Find the other face diagonals!
H
E
G
F
D
A
we can make?
C
B
From one vertex, how many face diagonals
How many face diagonals does the cube have?
Are they congruent?
If the length of its edge is s,
what is the length of its face diagonals?
CUBE
AG is called space diagonal (=diagonal ruang).
Find the other space diagonals!
H
E
G
F
D
A
we can make?
C
B
From one vertex, how many space diagonals
How many space diagonals does the cube have?
Are they congruent?
If the length of its edge is s,
what is the length of its space diagonals?
CUBE
ABGH is called diagonal plane (=bidang diagonal).
H
E
G
What is the shape of diagonal plane?
F
Can you find the other diagonal planes?
D
A
C
B
How many diagonal planes does the cube have?
Are they congruent?
CUBE
Dimension of diagonal plane:
H
E
G
F
D
A
G
H
face diagonal
C
B
A
B
edge
If the length of edge is ‘s’,
what is the area of diagonal plane?
CUBOID
W
T
V
U
S
P
R
Q
Cuboid is enclosed by 6 planes, which its base and top are
rectangular shaped.
The intersecting planes are perpendicular to each other.
CUBOID
W
V
T
U
S
R
P
vertex
face
Q
edge
How many vertices, edges,
and faces does the cube have?
CUBOID
W
T
V
U
S
P
The dimension of cuboid
Length
PQ, …, …, …
Width
TW, …, …, …
Height
VR, …, …, …
R
Q
CUBOID
W
V
U
T
S
P
R
Q
How many face diagonals
does cuboid have?
Are they congruent?
Let the length, width, and height are l, w, and h,
respectively.
What is the measurement of its face diagonals?
CUBOID
W
V
U
T
S
P
R
Q
How many space diagonals
does cuboid have?
Are they congruent?
Let the length, width, and height are l, w, and h,
respectively.
What is the measurement of its space diagonal?
CUBOID
W
V
U
T
S
P
R
Q
How many diagonal plane
does cuboid have?
Are they congruent?
What is the shape of cuboid’s diagonal plane?
Sketch all possible diagonal plane, determine its
measurement, and calculate the area of them.
PRISM
top
F
E
D
C
A
B
base
lateral
face
PRISM
A prism is a three dimensional shape that constructed of
TWO PARALLEL AND CONGRUENT POLYGONS
and the other faces are RECTANGLES or PARALLELOGRAMS.
F
F
E
D
D
C
A
E
C
B
Right prism
A
B
Oblique prism
PRISM
Regular triangular prism
Triangular prism
Pentagonal
(5-sided) prism
Rectangular prism
Hexagonal
(6-sided) prism
PRISM
Fill the table below, by investigating in your group discussion.
Kind of
prism
Figure
Vertex
Edges
Faces
Face
diagonal
Space
diagonal
Diagonal
plane
Triangular
prism
6
9
5
6
0
0
Rectangular
prism
8
12
6
12
4
6
Pentagonal
prism
10
15
7
20
10
5
Hexagonal
prism
12
18
8
30
18
15
PRISM
For n-sided based prism, we can conclude that:
The number of its vertices is
2n
The number of its edges is
3n
The number of its faces is
n+2
The number of its face diagonal is
n2 – n
The number of its space diagonal is
n2 – 3n
The number of its diagonal plane is
(n2 – n)/2; if n is even number or
(n2 – 3n)/2; if n is odd number
PYRAMID
top
lateral face
base
Pyramid is a polyhedral which enclosed by
A POLYGON AS ITS BASE and
TRIANGLES AS ITS LATERAL FACES.
PYRAMID
There are many kinds of pyramid, based on the shape of its base.
T
P
E
T
C
A
D
A
B
S
Triangular pyramid
R
B
C
Pentagonal pyramid
P
Q
Rectangular pyramid
PYRAMID
Fill the table below, by investigating in your group discussion.
Kind of
pyramid
Figure
Vertex
Edges
Faces
Face
diagonal
Space
diagonal
Diagonal
plane
Triangular
pyramid
4
6
4
0
0
0
Rectangular
pyramid
5
8
5
2
0
2
Pentagonal
pyramid
6
10
6
5
0
5
Hexagonal
pyramid
7
12
7
9
0
9
PYRAMID
For n-sided based pyramid, we can conclude that:
The number of its vertices is
n+1
The number of its edges is
2n
The number of its faces is
n+1
The number of its diagonal plane is (n2 – 3n)/2
Triangular shaped