We have used two different ways of solving for the surface area of a prism. The first is to break the prism up into a net and to find the area of each of the individual pieces. The second is to use a formula. Work through the following flashcards to practice finding the surface area of prisms.
Find the surface are of this triangular prism.
First, find the area of the base.
\(\mathsf{ B = \frac{1}{2}(b)(h) = \frac{1}{2}(3)(4) = 6 km^{2} }\)
Next, find the perimeter of the base.
\(\mathsf{ P = 3 + 4 + 5 = 12 km }\)
Finally, find the surface area.
\(\mathsf{ SA = 2B + ph }\)
\(\mathsf{ SA = 2(6) + 12(9) = 12 + 108 = 120 km^{2} }\)
Find the surface area of the rectangular prism below.
First, find the area of the base.
\(\mathsf{ B = l \times w = (12)(4) = 48in^{2} }\)
Next, find the perimeter of the base.
\(\mathsf{ P = 2(l) + 2(w) = 2(12) + 2(4) }\)
\(\mathsf{ P = 24 + 8 = 32 in }\)
Finally, calculate the surface area.
\(\mathsf{ SA = 2B + ph = 2(48) + 32(8) }\)
\(\mathsf{ SA = 96 + 256 = 352 in^{2} }\)
Find the surface area of this triangular prism.
First, find the area of the base.
\(\mathsf{ B = \frac{1}{2}(b)(h) = \frac{1}{2}(6)(4) = 12 m^{2} }\)
Next, find the perimeter of the base.
\(\mathsf{ P = 6 + 5 + 5 = 16 m }\)
Finally, find the surface area of the triangular prism.
\(\mathsf{ SA = 2B + ph = 2(12) + 16(7) }\)
\(\mathsf{ SA = 24 + 112 = 136 m^{2} }\)
Cards remaining:
