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

12×𝑟

=

=

=

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 ∆BAE, ∠A is right angle.

→→→→→

+

+

𝐵𝐸2=2×𝑟2

𝐵𝐸=√2×𝑟2𝐵𝐸=𝑟 √2

Diagonal

A B

CD

E

H

F

G

r cm

r cm

r cm

Look at ∆CAE, ∠A is right angle.

→→→→→

++

𝐶𝐸2=2𝑟 2+𝑟2=3𝑟2

𝐶𝐸=√3×𝑟2𝐶𝐸=𝑟 √3

Diagonal Plane

A B

C D

E

H

F

G

r cm

r cm

r cm

→→→

Look at rectangle ABGH

𝐴𝐵×𝐵𝐺

𝑟 ×𝑟 √2𝑟2√2

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 edges→12 x r = 12 x 4cm = 48 cm

b. The length of face diagonal→ r= 42 = = 32cm

c. The length of diagonal→ r= 43 = = 48cm

d. The area of diagonal plane→ = = 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 edges→12 x r = 12 x 6cm = 72 cm

b. The length of diagonal→ r= 63 = = 108cm

e. The area of diagonal plane→ = = 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( 𝑙+𝑤+h)

√𝑙2+𝑤2+h2

√𝑙2+𝑤2

√𝑙2+h2√𝑤2+h2

Example 1Example 2

Face/Plane Diagonal

A B

C D

E

H

F

G

l cmw cm

h cm

Look at ∆CBF, ∠B is right angle.

Look at ∆ABC, ∠B is right angle.

𝐶𝐹=√𝑤2+h2

+

+

𝐴𝐶=√𝑙2+𝑤2

+

+

Diagonal

A B

C D

E

H

F

G

l cmw cm

h cmLook at ∆CAE, ∠A is right angle.

→→→→

++

𝐶𝐸2=𝑙2+𝑤2+h2

𝐶𝐸=√𝑙2+𝑤2+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 …

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 – 18 = 5

Panjang diagonal ruang : :

: : : cm