12.3 Surface Areas of Prisms

Objectives: Find lateral areas of prisms Find surface areas of prisms

Characteristics of Prisms The bases are congruent faces in parallel planes The faces that are NOT bases are lateral faces The lateral faces intersect at the lateral edges. Lateral edges are parallel segments

Characteristics of Prisms Continued… A segment perpendicular to the bases with an endpoint on each plane is called and altitude of the prism. The height of the prism is the length of the altitude. A prism with lateral edges that are also altitudes is called a right prism. If the lateral edges are not perpendicular to the bases, it is an oblique prism.

Lateral Area L is the sum of the areas of the lateral faces L=ah+bh+ch+dh+eh+fh or L=h(a+b+c+d+e+f) or L=Ph

Key Concept #1: If a right prism has a lateral area of L square units, a height of h units, and each base has a perimeter of P units, then L=Ph

Example 1a: Find the lateral area of the figure to the right. L= Ph (Lateral area = perimeter of base x height) 2.L= (100)(7) 3.L= 700 Lateral area = 700 cm 2

Key Concept #2: If the surface area of a right prism is T square units, it height is h units, and each base has an area of B square units and a perimeter of P units, then T= L + 2B

Example 2a: Find the surface area of the figure to the right. 1.T= L + 2B 2.T= Ph + 2B 3.T= ( )16 + 2[1/2(4 x 3)] 4.T= (12)(16)+(6)(2) 5.T= T= 204 Surface Area = 204 mm 2

Example 2b: Find the surface area of the figure to the right. T= L+ 2B T= Ph + 2B T= ( )12 + (2)(3)(9) T= T= 342 The surface area = 342 in 2

Assignment: Pgs #6-21, 28, 29-33