CUBE and CUBOID
To calculate the sum of edges, length of face/plane diagonal, and diagonal, also area of diagonal plane
Created by Cep Andi Alim Subarkah for mathlabsky.wordpress.com Created by Cep Andi Alim Subarkah for mathlabsky.wordpress.com
CUBEThe sum of Edge
The length of face diagonal
The length of diagonal
The area of diagonal plane
12Γπ
=
=
=
A B
C D
E
H
F
G
r cm
r cm
r cm
EXAMPLE 1
EXAMPLE 2
Face/Plane Diagonal
A B
CD
E
H
F
G
r cm
r cm
r cm
Look at βBAE, β A is right angle.
βββββ
+
+
π΅πΈ2=2Γπ2
π΅πΈ=β2Γπ2π΅πΈ=π β2
Diagonal
A B
CD
E
H
F
G
r cm
r cm
r cm
Look at βCAE, β A is right angle.
βββββ
++
πΆπΈ2=2π 2+π2=3π2
πΆπΈ=β3Γπ2πΆπΈ=π β3
Diagonal Plane
A B
C D
E
H
F
G
r cm
r cm
r cm
βββ
Look at rectangle ABGH
π΄π΅Γπ΅πΊ
π Γπ β2π2β2
EXAMPLE 1Given a cube with measure of edge is 4 cm. calculatea. The sum of edges c. The length of diagonalb. The length of face diagonal d. The area of diagonal plane
The answer:
a. The sum of edgesβ12 x r = 12 x 4cm = 48 cm
b. The length of face diagonalβ r= 42 = = 32cm
c. The length of diagonalβ r= 43 = = 48cm
d. The area of diagonal planeβ = = cm2
EXAMPLE 2Given a cube with measure of face diagonal is cm. calculatea. The sum of edges c. The area of diagonal planeb. The length of diagonal
The answer:
L.O.F.D = r = r = : r = r = 6 cm
a. The sum of edgesβ12 x r = 12 x 6cm = 72 cm
b. The length of diagonalβ r= 63 = = 108cm
e. The area of diagonal planeβ = = cm2
CUBOID
A B
C D
E
H
F
G
l cmw cm
h cm
The sum of Edge
The length of face diagonal
The length of diagonal
4( π+π€+h)
βπ2+π€2+h2
βπ2+π€2
βπ2+h2βπ€2+h2
Example 1Example 2
Face/Plane Diagonal
A B
C D
E
H
F
G
l cmw cm
h cm
Look at βCBF, β B is right angle.
Look at βABC, β B is right angle.
πΆπΉ=βπ€2+h2
+
+
π΄πΆ=βπ2+π€2
+
+
Diagonal
A B
C D
E
H
F
G
l cmw cm
h cmLook at βCAE, β A is right angle.
ββββ
++
πΆπΈ2=π2+π€2+h2
πΆπΈ=βπ2+π€2+h2
EXAMPLE 1
Given a cuboid. Calculatea. The sum of edges
b. Face diagonal on basedc. The diagonal
The answer :
a. The sum of edges
: 4 (l + w + h): 4 (10 + 6 + 9): 4 (25): 100 cm
A B
CD
EF
GH
10 cm6 cm
9 cm
b. Length of : : : :
A B
CD
EF
GH
10 cm6 cm
9 cmc. The face diagonal on based
: : : :
d. The diagonal :
: : :
EXAMPLE 2
Sebuah balok memiliki ukuran rusuk alas 8 cm x 10cm. Jika panjang seluruh rusuk balok adalah 92cm, maka panjang diagonal ruang balok adalah β¦
Jawab
Panjang rusuk Seluruh = 92 4 (p + l + t) = 92 4 (8 + 10 + t) = 92 4 (18 + t) = 92 18 + t = 92 : 4 = 23 t = 23 β 18 = 5
Panjang diagonal ruang : :
: : : cm
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