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Prepared by:Prepared by:Mr. Albert F. PerezMr. Albert F. Perez
Define a prism and identify it’s properties.
Calculate the lateral area and surface area of right prisms.
Apply formulas for lateral and surface area to real situations.
A prism is a polyhedron
with two identical polygonal
faces,called bases,that lie
in parallel planes.
vertex
Lateraledge
base
lateral face
base
Click the part of the prism that you
want to know.
Altitude
The two parallel and congruent faces are called bases.
A
B
C
D
E
F
G
H I
J
Planes AIHGD and JFECB are bases
Lateral edge is a segment joining the vertex of a prism and any vertex of its base.
A
B
C
D
E
F
GH I
J
HF,GE,DC,AB, and I J are lateral edges.
Lateral face is one of the parallelogram-shaped faces of the prism that connect the bases.
A
B
C
D
E
F
G
H I
J
Planes GDEC,ABCD,ABJI,FHIJ,and FHGE are lateral faces.
Vertex is a point of intersection of the edges.
A
B
C
D
E
F
G
H I
J
Points A, B, C, D, E, F, G, H, I, J, are the vertices of a prism.
An altitude of a prism is a segment that is perpendicular to both bases with endpoints in the planes of the bases.
The height (h) of the prism is the length of the altitude
height
Types of Prism
Right prism
Oblique prism
Oblique Pentagonal prism
Oblique rectangular prism
These are oblique prisms.
cube
Triangular prism
Pentagonal prism
Rectangular prism
These are right prisms.
A
B
C
D
E F
“This is a net showing the lateral area of a prism.”
B
A
C
FE
D
B
A
C
FE
D
“The sum of areas A, E C, and F is the lateral area of the prism.”
“Lateral Area = A + C + F + E.=(8cm)(5cm)+(8cm)(5cm)+(4cm)(5cm)+(4cm)(5cm)= 5cm ( 8cm + 8cm + 4cm + 4cm)= 5cm [2(8cm) + 2(4cm)]Think: 5cm is the height of the prism 2(8cm) + 2(4cm) is the perimeter of the base.”
5cm
B
A
C
FE
D
8cm
5cm
4cm
8cm
4cm
LA = ph
5cm2cm
3cm
LA = [2(5cm) + 2(2cm)] [3cm]
LA =42cm2
The lateral area (LA) of a right prism is the product of the perimeter of its base and the height of the prism.
“This is a net showing the surface area of a prism.”
B
A
C
FE
D
A
B
C
D
E F
“Surface Area = A + C + F + E + B + D = ph + (8cm)(4cm) + (8cm)(4cm)
= ph + 2[(8cm)(4cm)]Think: (8cm)(4cm) is the area of the base of the prism.
B
A
C
FE
D
8cm 5cm
4cm
8cm
4cm
5cm
4cm
8cm
SA = LA + 2B
SA= 42cm2 + 2(10cm2)SA=62cm2
5cm2cm
3cm
The surface area (SA) of a prism is the sum of the lateral area and the areas of the two bases.
Find the lateral area of the right triangular prism.
Find the surface area of the prism.
SA = LA + 2B Solution:SA = 216+2(1/2)(8)(6) = 216+48=264 cm 2
6cm8cm
9cm
10cm
LA = ph Solution: LA =(6+8+10)(9)=216cm2
Find the lateral area and the surface area of the right equilateral triangular-based prism shown, if AB =14 and AD=20.
BB
D
C
Ax
Solution:LA = ph = (14+14+14)(20) = (42)(20) = 840 sq.unitsSA = ph + 2B = 840 + 2(1/2•14•7√3 ) = 840 + 98√3 sq.units
Find the altitude of a right prism for which the area of the lateral surface is 143 sq. units and the perimeter of the base is 13units.
Given:LA = 143 sq.units , perimeter = 13Altitude = ?Solution: LA = ph 143 = (13) h 11 = h
GF
D
HE
BA
C
Choose the letter of the best answer. Use the figure above.1. Plane ABCD is a _______.
2.Which is NOT a lateral edge?
c.baseb. face
a. Lateral face
b.AD
c.DGa.BE
Choose the letter of thebest answer.
5. The two bases of a prism _____ differ in their total number of edges.
a.always b.sometimes c.never
3. The lateral faces of a right prism are _____ rectangles.
a.always b.sometimes c.never
a.always b.sometimes c.never
4. The altitude of a right prism is ______ the height of the prism.
1.The lateral faces of a cube are squares. Find the surface area of a cube whose base edge length is 5 cm.
2.The perimeter of a base of a right prism is 37 cm and a lateral edge is 22 cm. Find the lateral area of the prism.
a. 150 cm2
b. 250 cm2
c. 200 cm2
a. 840 cm2
c. 814 cm2b. 850 cm2
Click the letter of the correct Click the letter of the correct answer.answer.
3.The surface area of a cube is 294 cm2.What is the length of its side?
b. 7 cma. 49 cm
c. 17 cm
4. Find the lateral area of a right triangular prism with a height of 20 in and a right triangular base with legs of 8 in and 6 in.
b. 490 in2a. 528 in2 c. 480 in2
Click the letter of the correct Click the letter of the correct answer.answer.
5. Many baking pans are given special coating to make food stick to the surface less. A rectangular cake pan is 9in by 13in and 2in deep.What is the area of the surface to be coated?
a. 234 in2 b. 250 in2 c. 205 in2
Click the letter of the correct Click the letter of the correct answer.answer.
6.How many square meters of fabric do you need to cover a suitcase with dimensions 0.9m by 0.7m by 0.2 m?
a. 19 m2
b. 1.9 m2
c. 0.19 m2
Click the letter of the correct Click the letter of the correct answer.answer.
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