1. by Maria Gloria G. Gabunada
BSEd – Math 4
2011 – 2012

2. What is a
?

3. What is a ?
Is the sum of the
areas of all the
faces of a solid.

4. What is a ?
The unit for surface
area is expressed in
square units.

7. Recall:
• A rectangular prism is
a solid (3-dimensional)
object which has six
faces that are
rectangles.
• Area of a rectangular
prism is given by the
formula:
– A = LW

8. Length (L)
Width (W)
A1 = LW
H A2 = L H
Height (H)
W A3 = LW W
A4 = L H
L

9. To get the surface area of a rectangular
Length (L) prism (SAr):
Width (W)
SAr = A1 + A2 + A3 + A4 + A5 + A6
A1 = LW
H A2 = L H
Height (H)
W A3 = LW W
A4 = L H
L

10. To get the surface area of a rectangular
Length (L) prism (SAr):
Width (W)
SAr = A1 + A2 + A3 + A4 + A5 + A6
A1 = LW
Note: A1 = A3 ; A2 = A4 ; A5 = A6
H A2 = L H
Height (H)
SAr = 2A1 + 2A2 + 2A5
W A3 = LW W
A4 = L H
L

11. To get the surface area of a rectangular
Length (L) prism (SAr):
Width (W)
SAr = A1 + A2 + A3 + A4 + A5 + A6
A1 = LW
Note: A1 = A3 ; A2 = A4 ; A5 = A6
H A2 = L H
Height (H)
SAr = 2A1 + 2A2 + 2A5
W A3 = LW W
By substitution, we get
A4 = L H
L

12. Example #1:
• Find the surface area of
a rectangular prism
whose length measures
7cm., width which
measures 4cm. , and
height which measures
2.5cm.

13. Example #1:
• Find the surface area of
a rectangular prism
whose length measures
H = 2.5cm
7cm., width which
measures 4cm. , and
height which measures
2.5cm.

14. Example #1: H = 2.5cm
• Find the surface area of a
rectangular prism whose length
measures 7cm., width which
measures 4cm. , and height
which measures 2.5cm.

15. Solution #1:
H = 2.5cm
SAr = 2LW +2WH + 2LH
SAr = 2(7cm)(4cm) +
2(4cm)(2.5cm) +
2(7cm)(2.5cm)
Example #1:
• Find the surface area of a SAr= 56cm2 + 20cm2 + 35cm2
rectangular prism whose length
measures 7cm., width which
measures 4cm. , and height SAr = 111 cm2
which measures 2.5cm.

18. Recall:
• a cube is a three-
dimensional solid
object bounded by six
square faces.
• Area of a square is
given by the formula:
– A = S2

19. To get the surface area of a cube Sac:
As = S2
SAs = S2 + S2 + S2 + S2 + S2 + S2
As = S 2 As = S 2 As = S 2
As = S 2
As = S 2

20. To get the surface area of a cube Sac:
As = S2
SAs = S2 + S2 + S2 + S2 + S2 + S2
As = S 2 As = S 2 As = S 2
By simplifying, we get
As = S 2
As = S 2

21. Example #2:
• find the surface area of a
cube whose sides measure
3in.

22. Example #2:
• find the surface area of a
cube whose sides measure
3in.
S = 3inches

23. Example #2:
• find the surface area of a
cube whose sides measure
3in.
Solution #2: S = 3inches
SA s = 6S2
SA s = 6(3in)2
SA s = 54in2

26. Notice:
• It has a flat base and a
flat top
• The base is the same as
the top, and also in-
between
• Because it has a curved
surface it is not a
polyhedron.

27. • When we cut the body of a
cylinder, we obtain a rectangle.
– The formula for the area of a
Ac =πr2 rectangle (Ar) is LxW
• A right circular cylinder has 2
circular bases.
Ar = 2πrh – The formula for the area of a circle
(Ac) is πr2
• The length of the body of the
Ac =πr2
cylinder is equal to the
circumference of its circular
bases.
– L = 2πr
– W = h (for height)
• Ar = 2πrh

28. To get the surface area of a right
circular cylinder
SA c = 2Ac + Ar
Ac =πr2 SA c = 2πr2 + LW
SA c = 2πr2 + 2πrh
Ar = 2πrh
Ac =πr2

29. To get the surface area of a right
circular cylinder
SA c = 2Ac + Ar
Ac =πr2 SA c = 2πr2 + LW
SA c = 2πr2 + 2πrh
Ar = 2πrh
By simplification, we obtain
Ac =πr2

30. Example #3:
• find the surface area of a
right circular cylinder with a
radius of 1.5 inches and a
height of 5.2 inches.

31. Example #3:
• find the surface area of a
r = 1.5in. right circular cylinder with a
radius of 1.5 inches and a
height of 5.2 inches.
h = 5.2in.

32. Example #3:
• find the surface area of a
r = 1.5in. right circular cylinder with a
radius of 1.5 inches and a
height of 5.2 inches.
h = 5.2in.
Solution #3:
SA = 2π(r + h)
SA s = 2π(1.5in.)(1.5in.+ 5.2in.)
SA s = 3πin.(6.7in.)
SA s = 201πin2

34. • Units count. Use the same units for
all measurements.
• Surface Area of any prism is given by:
Lateral area + Area of two ends