surface area of rectangular prisms. total surface area is the combined area of all faces of a solid....
TRANSCRIPT
Surface Area of Rectangular
Prisms
• Total surface area is the combined area of ALL faces of a solid.
• To calculate total surface area (S), you can find the area of each face (including the bases) and add all the area measures.
5
23
5(2)
=
10
Calculate the total surface area of the prism.
5(2)
=
10
5(3)
=
15
5(3)
=
15
3(2) = 6
3(2) = 6
2(10) + 2(15) + 2(6) = 62 units²
You can also use a formula to calculate total surface area of prisms.
S = Ph + 2BPerimeter of the Base
Area of the Base
Height of prism
5
23
P = 3 + 2 + 3 + 2P = 10
B = lwB = 3(2)B = 6
S = Ph + 2BS = 10(5) + 2(6)S = 62 units²
First, find P.
Then, find B.
Finally, plug your calculations for P and B into the formula for surface area.
Eric wants to wrap his mom’s Christmas present. The box is 10 inches tall, 8 inches wide, and 6 inches long. How much paper will he need to cover the box?
10”
6”8”
P = 8 + 6 + 8 + 6
P = 28
B = lwB = 8(6) B = 48
S = Ph + 2B S = 28(10) + 2(48) S = 376 inches²
Lateral area is the surface of a solid, excluding the bases.
Lateral, lateral, lateral is the label, label, label…
To find the lateral surface area, you can calculate the area of each lateral face, or you can use this formula:
LA = PhPerimeter of the Base Height of prism
Find the lateral surface area.
First, find P.
P = 2 + 2 + 2 + 2P = 8
2
220
LA = Ph
LA = 8(20)
LA = 160 units²
Then, multiply P by the height of the prism.