Rectangular Prisms are made up of 6 6 different rectangles. When faced with an exercise or exam that asks you to calculate the surface area of a rectangular Prism, use the formula below.

The formula: how to calculate the area of a rectangular prism (rectangular orthohedron)?

S=2×(Width×Length+Height×Width+Height×Length) S=2 \times (Width \times Length+ Height \times Width + Height\times Length)

S= surface area

how to calculate the area of a rectangular prism (rectangular orthohedron)

Suggested Topics to Practice in Advance

  1. Parts of a Rectangular Prism
  2. Cuboids
  3. How to calculate the volume of a rectangular prism (orthohedron)

Practice Surface Area of a Cuboid

Examples with solutions for Surface Area of a Cuboid

Exercise #1

A cuboid has the dimensions shown in the diagram below.

Which rectangles form the cuboid?

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Video Solution

Step-by-Step Solution

Every cuboid is made up of rectangles. These rectangles are the faces of the cuboid.

As we know that in a rectangle the parallel faces are equal to each other, we can conclude that for each face found there will be two rectangles.

 

Let's first look at the face painted orange,

It has width and height, 5 and 3, so we already know that they are two rectangles of size 5x6

 

Now let's look at the side faces, they also have a height of 3, but their width is 6,

And then we understand that there are two more rectangles of 3x6

 

Now let's look at the top and bottom faces, we see that their dimensions are 5 and 6,

Therefore, there are two more rectangles that are size 5x6

 

That is, there are
2 rectangles 5X6

2 rectangles 3X5

2 rectangles 6X3

Answer

Two 5X6 rectangles

Two 3X5 rectangles

Two 6X3 rectangles

Exercise #2

A cuboid is shown below:

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What is the surface area of the cuboid?

Video Solution

Step-by-Step Solution

Remember that the formula for the surface area of a cuboid is:

(length X width + length X height + width X height) 2

 

We input the known data into the formula:

2*(3*2+2*5+3*5)

2*(6+10+15)

2*31 = 62

Answer

62

Exercise #3

Look at the cuboid below.

888555121212

What is the surface area of the cuboid?

Video Solution

Step-by-Step Solution

Let's see what rectangles we have:

8*5

8*12

5*12

Let's review the formula for the surface area of a rectangular prism:

(length X width + length X height + width X height) * 2

Now let's substitute all this into the exercise:

(8*5+12*8+12*5)*2=
(40+96+60)*2=
196*2= 392

This is the solution!
 

Answer

392 cm²

Exercise #4

Look at the cuboid below.

What is its surface area?

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Video Solution

Step-by-Step Solution

We identified that the faces are

3*3, 3*11, 11*3
As the opposite faces of an cuboid are equal, we know that for each face we find there is another face, therefore:

3*3, 3*11, 11*3

or

(3*3, 3*11, 11*3 ) *2

 

To find the surface area, we will have to add up all these areas, therefore:

(3*3+3*11+11*3 )*2

 

And this is actually the formula for the surface area!

We calculate:

(9+33+33)*2

(75)*2

150

Answer

150

Exercise #5

Look at the the cuboid below.

What is its surface area?

333555888

Video Solution

Step-by-Step Solution

First, we recall the formula for the surface area of a cuboid:

(width*length + height*width + height*length) *2

 

As in the cuboid the opposite faces are equal to each other, the given data is sufficient to arrive at a solution.

We replace the data in the formula:

 

(8*5+3*5+8*3) *2 =

(40+15+24) *2 =

79*2 = 

158

Answer

158

Exercise #6

Look at the cuboid of the figure.

Its surface area is 122 cm².

What is the width of the cuboid?

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Video Solution

Step-by-Step Solution

To solve the problem, let's recall the formula for calculating the surface area of a box:

(width*length + height*width + height*length) *2

Let's substitute the known values into the formula, and we'll denote the missing side as X:

2*(3*7+7*X+3*X) = 122

2*(21+7x+3x) = 122

2(21+10x) = 122

Let's expand the parentheses:

42+20x=122

Let's move terms:

20x=122-42

20x=80

Let's simplify:

x=4

And that's the solution!

Answer

4 cm

Exercise #7

An unfolded cuboid is shown below.

What is the surface area of the cuboid?

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Video Solution

Step-by-Step Solution

To calculate the surface area of the rectangular prism, we will need to identify its three faces (each face appears twice):

1*3

1*8

3*8

 

The formula for the surface area of a rectangular prism is the sum of all the areas of the faces, that is:

We replace the data in the formula:

2*(1*3+1*8+3*8)=
2*(3+8+24) = 
2*35 = 

70

And this is the solution!

Answer

70

Exercise #8

Given that the volume of the cuboid is equal to 72 cm³

The length of the cuboid is equal to 6 cm and the height is equal to half the length.

Calculate the surface of the cuboid

666

Video Solution

Step-by-Step Solution

The first step is to calculate the relevant data for all the components of the box.

The length of the box = 6

Given that the height of a cuboid is equal to half its length we are able to deduce the height of the box as follows : 6/2= 3

Hence the height = 3

In order to determine the width, we insert the known data into the formula for the volume of the box:

height*length*width = volume of the cuboid.

3*6*width = 72

18*width=72

We divide by 18:

Hence the width = 4

We are now able to return to the initial question regarding the surface of the cuboid.

Remember that the formula for the surface area is:

(height*length+height*width+length*width)*2

 

We insert the known data leaving us with the following result:

(3*6+4*3+4*6)*2=

(12+24+18)*2=

(54)*2=

108

Answer

108 cm²

Exercise #9

Which dimensions may represent a cuboid?

Step-by-Step Solution

There is no limitation or rule regarding the dimensions that a cuboid can have.

Therefore the correct answer is D.

Answer

All of the above.

Exercise #10

Calculate the surface area of the orthohedron below using the data in the diagram.

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Video Solution

Answer

62

Exercise #11

What is the surface area of the cuboid in the figure?

141414171717727272

Video Solution

Answer

4940

Exercise #12

A cuboid has a surface area of 102.

Calculate X.

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Video Solution

Answer

3

Exercise #13

A rectangular prism has a square base measuring 25 cm.

It has a height is equal to 3 cm.

Calculate the surface area of the rectangular prism.

333

Video Solution

Answer

110

Exercise #14

Calculate the surface area of the box shown in the diagram.

Pay attention to the units of measure!

5 dm5 dm5 dm4 cm4 cm4 cm0.3 dm0.3 dm0.3 dm

Video Solution

Answer

724

Exercise #15

Given the cuboid whose square base is of size 25 cm²,

The height of the cuboid is 3 cm,

333S=25

What is the surface area of the cuboid?

Video Solution

Answer

110 cm²

Topics learned in later sections

  1. Cubes