 # Surface Area of Prisms

Related Topics: More Geometry Lessons

In these lessons, we will learn how to
• calculate the surface area of prisms: rectangular prisms, triangular prisms, trapezoidal prisms, hexagonal prisms etc.
• calculate the surface area of prisms using nets.

What is a Prism?

A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. A prism is named after the shape of its base. The other faces are in the shape of parallelograms. They are called lateral faces.

The following diagrams show a triangular prism and a rectangular prism.  A right prism is a prism that has its bases perpendicular to its lateral surfaces.

When we cut a prism parallel to the base, we get a cross section of a prism. The cross section is congruent (same size and shape) as the base, as can be seen in the following diagram.  How to calculate the surface area of a prism?

The surface area of a prism is the total area of all its external faces.

Step 1 : Determine the shape of each face.
Step 2 : Calculate the area of each face.
Step 3 : Add up all the areas to get the total surface area.

We can also use the formula

Surface area of prism = 2 × area of base + perimeter of base × height

Worksheet to calculate the surface area and volume of a rectangular prism

Example:

Calculate the surface area of the following prism. Solution:

There are 2 triangles with the base = 4 cm and height = 3 cm. Area of the 2 bases = 12 cm2

1 rectangle with length = 7 cm and width = 5 cm
Area = lw = 7 × 5 = 35 cm2

1 rectangle with length = 7 cm and width 3 m
Area = lw = 7 × 3 = 21 cm2

1 rectangle with length = 7 cm and width 4 m
Area = lw = 7 × 4 = 28 cm2

The total surface area is 12 + 35 + 21 + 28 = 96 cm2

We can also use the formula
Surface area of prism = 2 × area of base + perimeter of base × height
= 2 × 6 + (3 + 4 + 5) × 7 = 96 cm2

Example:

The diagram shows a prism whose base is a trapezoid. The surface area of the trapezoidal prism is 72 cm2. Find the value of x.  Solution:

There are 2 rectangles with length = 5 cm and width = 3 cm
Area = 2 × 5 × 3 = 30 cm2

There is one rectangle with length = 5 cm and width = 4 cm
Area = 5 × 4 = 20 cm2

There is one rectangle with length = 5 cm and width = 2 cm
Area = 5 × 2 = 10 cm2

There are two trapezoids.
Area = cm2 = 6x cm2

Sum of area
30 + 20 + 10 + 6x = 72
60 + 6x = 72
x = 2

The value of x is 2.

### How to find the Surface Area of different types of Prisms

This video shows how to find the surface area of prisms: cuboid (or rectangular prism), triangular prism, trapezoidal prism. How to find the surface area of a rectangular prism? How to find the surface area of a triangular prism using the formula SA = ab+(s1+s2+s3)h? How to find the surface area of a pentagonal prism? How to find the surface area of a hexagonal prism? How to find the surface area of a octagonal prism?

How to find the surface area of prisms and cylinders using a given formula? How to solve word problems and composite figures?
Problem: A treasure chest is a composite figure. If you were to paint the surface area, how many square feet would you paint? Round your answer to the nearest feet.

### Surface area of prisms using nets

This video shows how to find the surface area of a cube, rectangular prism and triangular prism using nets. How to find the surface area of a hexagonal prism using a net?

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