Surface Area of Rectangular Prisms
Concept
There are two types of areas, the lateral surface area of the prism, and second, the total surface area of the prism. The lateral area of a prism is the sum of the areas of all its lateral faces whereas the total surface area of a prism is the sum of its lateral area and area of its bases.
The total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.
Rules
1. Determine the length, width, and height of the prism.
2. A rectangular prism has 6 rectangular faces. To find the surface area of a rectangular prism, add the areas of all 6 faces.
3. The surface area of a rectangular prism can be found using the formula, S.A. = 2(lw + wh + lh)
4. Write the answer with the appropriate square units.
Example
What is the surface area of the rectangular prism?
Solution
Method 1
Surface Area = Sum of the areas of all faces
Top face = 6 cm x 2 cm = 12 cm2
Bottom face = 12 cm2
Right face = 4 cm x 2 cm = 8 cm2
Left face = 8 cm2
Front face = 4 cm x 6 cm = 24 cm2
Back face = 24 cm2
Total Surface Area = 12 cm2 + 12 cm2 + 8 cm2 + 8 cm2 + 24 cm2 + 24 cm2
Total Surface Area = 88 cm2
Method 2
Surface Area = 2lw + 2lh + 2hw
= 2(6 cm x 2 cm) + 2 (6 cm x 4 cm) + 2 (4 cm x 2 cm)
= 24 cm2 + 48 cm2 + 16 cm2
= 88 cm2
Practice Surface Area of Rectangular Prisms
Practice Problem 1
What is the surface area of the rectangular prism, shown below with its net?
Practice Problem 2
What is the surface area of the rectangular prism?
Practice Problem 3
Terry built a toy box 60 inches long, 24 inches wide, and 36 inches high. How much paint does he need to paint the outside of the box?
Net: A two-dimensional shape that can be modified to form a three-dimensional shape or a solid. A 3-D shape may have different nets.
Surface area: It is the sum of the areas of all the surfaces of a three-dimensional figure.
Lateral area: It is the surface area of the figure, excluding the area of the base(s) of a three-dimensional figure.
Prism: A prism is a three-dimensional solid which has identical faces at both ends. The other faces are flats. A prism is named after its base.
Rectangular Prism: A solid (3-dimensional) object which has six faces that are rectangles. It has the same cross-section along a length, which makes it a prism.