1. Areas and Volumes of Prisms
Section 12.1
Areas and Volumes of Prisms

2. PRISMS

3. What is a prism?
A prism is a polyhedron with a pair of congruent bases, that lie in parallel planes.
The vertices of the bases are joined to form the lateral faces of a prism.
Prisms are named according to the shapes of their bases.

4. PARTS of a PRISM
FACE
BASE
HEIGHT
FACE
BASE
HEIGHT

5. CROSS SECTIONS
What is a cross section?

6. Right vs. Oblique
If the lateral edges of a prism are perpendicular to its bases, the prism is a right prism.
If the lateral edges of a prism are not perpendicular to the bases, the prism is an oblique prism.

7. Right Prisms vs. Oblique Prisms

8. L.A. = ph LATERAL AREA p = perimeter of the base
h = height of the prism

9. TOTAL AREA
The sum of the areas of each face.
T.A. = L.A. + 2B

10. VOLUME of a PRISM
V = Bh
B = area of the Base
h = height of the prism

11. A right trapezoidal prism is shown
A right trapezoidal prism is shown. Find the lateral area, total area, and volume.
Height of trapezoidal base
Height of prism

12. LA = ph TA = LA + 2B p = 12 + 6 + 5 + 5 = 28 h = 10 LA = 28 ∙ 10 = 280
TA = LA + 2(½h(b1 + b2))
h = 10
TA = 280+2(½∙4(12+6 ))
LA = 28 ∙ 10 = 280
TA = 280+2(2(18 ))
TA = 280+2(36)
TA =
TA = 352
V = Bh
V = (½h(b1 + b2)) h
V = (½·4(12+6)) 10
V = (2(18)) 10
V = (36) 10
V = 360

13. A right triangular prism is shown
A right triangular prism is shown. Find the lateral area and total area since the volume = 315.

14. V = Bh TA = LA + 2B 315 = Bh 315 = (½bh)h 315 = (½·10.5·4)h
TA = LA + 2(½bh)
315 = (½bh)h
TA = (½·10.5·4)
315 = (½·10.5·4)h
TA = (21)
315 = (21)h
TA =
15 = h
TA = 402
LA = ph
p = =24
h = 15
LA = 24·15
LA = 360