Surface Area of Triangular 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 surface area of a triangular prism is also referred to as its total surface area. The total surface area of a triangular prism is the sum of the areas of all the faces or surfaces of the prism. A triangular prism has three rectangular faces and two triangular faces. The rectangular faces are said to be the lateral faces, while the triangular faces are called bases. If the bases of a triangular prism are placed horizontally, they are referred to as the top and the bottom (faces) of the prism, respectively.
Rules
1. Find the area of the two triangular faces. They will have the same area, so you can find one area and multiply by 2.
2. Find the area of each of the rectangular face. Those faces may all have different areas.
3. Add all five areas together and express the answer in the proper square units.
Example
Find the surface area.
Solution
Area of two triangular faces:
=
=
= 48 cm2
Area of rectangular faces:
Face 1: l x w = 6 x 12 = 72 cm2
Face 2: l x w = 8 x 12 = 96 cm2
Face 3: l x w = 10 x 12 = 120 cm2
Total surface area:
48 cm2 + 72 cm2 + 96 cm2 + 120 cm2
= 336 cm2
Practice Surface Area of Triangular Prisms
Practice Problem 1
From the choices below, select the correct calculation for finding the surface area of this prism.
Practice Problem 2
Find the surface area.
Practice Problem 3
Juliane needs to paint the roof of a dog house. Dimensions are shown below. How many cans of paint does she need if for 1 can of paint she can paint 0.25m2?
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.
Triangular Prism: A triangular prism is a polyhedron, made up of two triangular bases and three rectangular sides.