Chapter 12 Notes: Surface Area and Volume of Prisms

Goal: Students will find the surface area and volume of prisms.

• A prism is a polyhedron with two congruent faces, called bases, that lie in parallel planes.

• The other faces, called lateral faces, are parallelograms formed by connecting the corresponding vertices of the bases.

• The segments connecting these vertices are lateral edges.

• Prisms are classified by the shapes of their bases.

• Right Prisms:

• The height of a prism is the perpendicular distance between its bases, called an altitude.

• A prism may be either right or oblique.

• In a right prism, each lateral edge is perpendicular to both bases.

• A prism with lateral edges that are not perpendicular to the bases is an oblique prism.

• Theorem 12.2 Surface Area of a Right Prism:– The lateral area of a prism is the sum of the

areas of the lateral faces.

– The surface area of a prism is the sum of the areas of the lateral faces and the two bases.

Lateral Area: L.A = ph

Surface Area: S = ph + 2B

where P is the perimeter of the base, h is the height of the prism, and B is the area of the

base.

Ex.1: Find (a) the lateral area, and (b) the surface area of the prism.

3 cm 4 cm

6 cm

Ex.2: Find the lateral area and surface area of a right rectangular prism with height 7 inches, length 3 inches, and width 4 inches.

Ex.3: Find the surface area of the right pentagonal prism.

Volume of Prisms

• Postulate 27 Volume of a Cube:

V = s3

where s is the length of the base edge.

Ex.4: Find the volume of a cube that has a side length of 6 cm.

• Theorem 12.6 Volume of a Prism:

Volume: V = Bh

where B is the area of the base, and h is the height of the prism.

• Find the volume of the solid.

Ex.5:

Ex.6: 10 cm

20 cm

24 cm

Ex.7:

10 in

8 in

8 in

8 in

Ex.8: The volume of a triangular prism is 1860 cm3. Its base is a right triangle with legs 24 cm and 10 cm long.

a. Draw and label a diagram.

b. Find the area of the base of the prism.

c. Find the height of the prism.

Ex.9: The volume of the cube is 90 cubic inches. Find the value of x.

Ex.10: Find the volume of the right hexagonal prism.

Ex.11: Find the volume of the puzzle piece in cubic units.

Ex.12: Find the surface area of the solid formed by the net. Round your answer to two decimal places.