4-4 Surface Area of Prisms & Pyramids

1. Prisms: The surface area of a prism is the total area of the surface of the object. To calculate the surface area, find the area of each face and add them up.

a)  Rectangular prism: Draw each surface and calculate the surface area.

Top / Bottom / Front & Back / Sides
A = bh
A = (90)(130)
A = 11700 cm2 / A = bh
A = (90)(50)
A = 4500 cm2 / A = bh
A = (130)(50)
A = 6500 cm2

Now add the area of all faces to find the surface area.

Surface Area = 2(Top/Bottom) + 2(Front/Back) + 2(Sides) Q: How many faces in total? = 2(11700) + 2(4500) + 2(6500)

= 45 400 cm2

b) Triangular Prism: Draw each surface and calculate the surface area.

Ends ∆ / Face 1 / Face 2 / Face 3
A = bh¸ 2
A = (1.2)(0.5) ¸ 2
A = 0.3 m2 / A = bh
A = (1.3)(2.1)
A = 2.73 m2 / A = bh
A = (2.1)(0.5)
A = 1.05 m2 / A=bh
A = (2.1)(1.2)
A = 2.52 m2

Surface Area = 2(Ends) + Face 1 + Face 2+ Face 3 Q: How many faces in total?

= 2(0.3) + 2.73 + 1.05 + 2.52

= 6.9 m2

2. Pyramids: The surface area of a pyramid is the total area of the surface of the object. To calculate the surface area, find the area of each face and add them up.

a) Square-based pyramids: Draw each surface and calculate the surface area.

Base / Faces ∆ / Surface Area
A = s2
A = (4)(4)
A = 16 cm2 / A = bh ¸ 2
A = (4)(3) ¸ 2
A = 6 cm2 / = Base + 4(Faces)
= 16 + 4(6)
= 40 cm2

Q: How many faces?