how to find the surface area of a rectangular prism

Related Pages
Surface Area Formulas
Surface Area of Cuboids
Surface Area of a Sphere
More Geometry Lessons

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.

triangular 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.

cross section prism

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.

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How To Find The Surface Area Of A Rectangular Prism?

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How To Find The Surface Area Of A Triangular Prism Using The Formula SA = ab+(s1+s2+s3)h?

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How To Find The Surface Area Of A Pentagonal Prism?

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How To Find The Surface Area Of A Hexagonal Prism?

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How To Find The Surface Area Of A Octagonal Prism?

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Word Problems About Prisms

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 square feet.

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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.

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How To Find The Surface Area Of A Hexagonal Prism Using A Net?

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