Rectangular Prisms are made up of 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.
Rectangular Prisms are made up of 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.
S= surface area
A cuboid has the dimensions shown in the diagram below.
Which rectangles form the cuboid?
If we take as an example an orthohedron with the following characteristics, its surface area will be calculated as follows:
Width = cm
Length = cm
Height = cm
Now, we apply the formula:
Thus, by solving the exercise we will obtain that the surface area of the rectangular prism (orthohedron) is cm².
If this exercise is easy for you and you are interested in learning how to calculate the surface area of a prism, you can learn it in the following article: Surface area of triangular prisms.
It is important to remember that in the exam the name of the shape may vary from one exercise to another.
For example: Rectangular Prism, Orthohedron and Cube.
Soit is important to remember that it is a geometric shape with faces, Edges and Vertices.
What is our conclusion?
That the surface area of a rectangular prism (orthohedron) is the sum of the areas of all the rectangles that form it.
Throughout primary and secondary school, you will have to deal with exercises of all kinds related to the field of geometry. So you will need to know how to calculate the surface area of a rectangular prism. We present you the formula that will help you to do it and give you some tips to internalize the learned materials in a better way.
If we take as an example a rectangular prism with the following characteristics, its surface area will be calculated as follows:
Width cm
Length cm
Height cm
The surface area of the rectangular prism is:
A that the surface area of an orthohedron is the sum of the areas of all the rectangles that form it. Let's see it illustrated in the following picture:
Answer:
Thus, by solving the exercise we will obtain that the surface area of the rectangular prism is cm².
What is our conclusion?
If you are interested in this article you may also be interested in the following articles:
Orthohedron - rectangular prism
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Given two orthohedra
Task:
Are the surfaces of the two orthohedra the same or different?
Solution:
Let's observe that the orthohedra are identical, they are just presented differently.
If we turn one of them upside down, it will be clear that the cubes are identical.
We can verify by calculus.
Right orthohedron :
Left Orthohedron :
Answer:
The surfaces are equal.
A cuboid is shown below:
What is the surface area of the cuboid?
Calculate the surface area of the orthohedron below using the data in the diagram.
Given the cuboid in the drawing, what is the appropriate unfolding?
Given that the area of the orthohedron is equal to cm².
The height of the orthohedron is equal to cm and the width is cm.
Calculate the volume of the orthohedron
Task:
Calculate the volume of the orthohedron.
Solution:
Area = cm²
Length = cm
Width = cm
Height =
Replace the height by
/ :divide into
The length is equal to cm.
We replace it in the volume formula:
Answer:
The volume of the orthohedron is equal to cm³.
Given a cube with the following information:
Width cm
Length cm
Height cm
How to calculate the surface area of the cube.
Answer:
The surface area of the cube is: cm².
Look at the cuboid below.
What is the surface area of the cuboid?
Look at the cuboid below.
What is its surface area?
Look at the the cuboid below.
What is its surface area?
Given a rectangular prism with the following information:
Width cm
Length cm
Height cm
How to calculate the surface area of the rectangular prism.
Answer:
cm²
Given a rectangular prism with the following information:
Width cm
Length cm
Height cm
How to calculate the surface area of the rectangular prism.
Answer:
The surface area of the rectangular prism is: cm².
What is the surface area of the cuboid in the figure?
A cuboid has a surface area of 102.
Calculate X.
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.
To calculate the total area of a rectangular prism, we have to calculate the areas of each of its faces (6 faces) and then add the area of all of them to obtain the total area.
Factoring the
where:
Surface area
length
width
height
Calculate the surface area of the box shown in the diagram.
Pay attention to the units of measure!
Given the cuboid whose square base is of size 25 cm²,
The height of the cuboid is 3 cm,
What is the surface area of the cuboid?
Look at the cuboid of the figure.
Its surface area is 122 cm².
What is the width of the cuboid?
The area of a rectangular prism is calculated with the formula:
While the volume is calculated with the following formula:
Example
Let the following rectangular prism have the following dimensions
Width
Length
Height
Let's calculate the area with the formula
Now we calculate the volume
Result
To calculate the area of a rectangular box we add the areas of its six faces, or by using the following formula:
Where:
Surface area
length
width
height
The surface area of a cube is 24 cm². How long is the cube's side?
The surface area of the cuboid shown below is 147 cm².
What are the dimensions of the cuboid that are not labelled in the drawing?
A cuboid has the dimensions shown in the diagram below.
Which rectangles form the cuboid?
A cuboid has the dimensions shown in the diagram below.
Which rectangles form the cuboid?
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
Two 5X6 rectangles
Two 3X5 rectangles
Two 6X3 rectangles
A cuboid is shown below:
What is the surface area of the cuboid?
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
62
Look at the cuboid below.
What is the surface area of the cuboid?
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!
392 cm²
Look at the cuboid below.
What is its surface area?
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
150
Look at the the cuboid below.
What is its surface area?
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
158