Surface Area of Rectangular Prism Calculator
How to use the ‘Surface Area of Rectangular Prism Calculator’?
Follow the steps below to use the surface area of rectangular prism calculator:
Step 1: Toggle and select the option of your choice as ‘surface area’ or ‘ lateral surface area’ to calculate.
Step 2: Enter the known three measures into the respective input boxes and the unknown measure will be calculated.
Step 3: Select the appropriate units for the inputs and output.
Step 4: Click on the ‘Solve’ button to obtain the result.
Step 5: Click on the ‘Show steps’ button to know the stepwise solution to find the missing measure.
Step 6: Click on the button to enter new inputs and start again.
Step 7: Click on the ‘Example’ button to play with different random input values.
Step 8: Click on the ‘Explore’ button and define the dimensions of a rectangular prism with the use of slider and calculate the surface area or lateral surface area. Also, use the slider to close the net of a rectangular prism.
Step 9: When on the ‘Explore’ page, click the ‘Calculate’ button if you want to go back to the calculator.
What is Rectangular Prism?
A rectangular prism is a three-dimensional shape with a rectangular base and top along with the four lateral faces. All the faces of rectangular prism are rectangular. As a result, there are three pairs of identical faces that are top-base, right side-left side and front -back as seen in the picture below. A rectangular prism is also known as a cuboid because of its shape. Objects found in our daily lives like geometry boxes, notebooks, diaries, rooms,are commonly rectangular prism shaped. The shape of a rectangular prism can be seen in the diagram below.
Formulas Used for ‘Surface Area of a Rectangular Prism’
If length, width and height is given as input, surface area will be calculated.
\(SA = \left ( l \times w + w \times h+l \times h \right )\)
If height, width and surface area is given as input, length will be calculated.
\(l=\frac{(SA-2\times w\times h)}{2(w+h)}\)
If length, width and surface area is given as input, height will be calculated.
\(h=\frac{(SA-2\times l\times w)}{2(w+l)}\)
If length, height and surface area is given as input, width will be calculated.
\(w=\frac{(SA-2\times l\times h)}{2(h+l)}\)
Formula Used for ‘Lateral Surface Area’
If length, width and height is given as input, lateral surface area will be calculated.
\(LSA=2(wh+lh)\)
If height, width and lateral surface area is given as input, length will be calculated.
\(l=\frac{(LSA-2\times w \times h)}{2 \times h}\)
If length, width and lateral surface area is given as input, height will be calculated.
\(h=\frac{LSA}{2 (w+l)}\)
If length, height and lateral surface area is given as input, width will be calculated.
\(w=\frac{(LSA-2 \times l \times h)}{2\times h}\)
Solved Examples
Example 1: Length, width and height of a rectangular prism are 10 inches, 8 inches and 5 inches. Calculate the surface area of a prism.
Solution:
Use the formula for surface area,
\(SA=2\left ( l\times w + w \times h + l \times h\right )\)
\(SA=2\left ( 10\times 8 + 8 \times 5 + 10 \times 5\right )\)
\(SA= 34\text{ } in^{2}\)
So, the surface area of the rectangular prism is 340 square inches.
Example 2: Length, width and height of a rectangular prism are 12 centimeters, 9 centimeters and 6 centimeters. Calculate the lateral surface area of a prism.
Solution:
Use the formula for surface area,
\(LSA=2 (l \times h + w \times h)\)
\(LSA=2 (12 \times 6 + 9 \times 6)\)
\(LSA = 252 \text{ }cm^{2}\)
So, the lateral surface area of the rectangular prism is 252 square centimeters.
Example 3: If the base of a room has a dimension as \(15 ft \times 14 ft\), and the lateral surface area is 638 square feets. Calculate the height of a room.
Solution:
\(l= 15\text{ } ft\)
\(w = 14\text{ }ft\)
\(LSA = 368\text{ }ft^{2}\)
Rearrange the formula of LSA for h
\(h = \frac{LSA}{2(w+l)}\)
\(h=\frac{638}{2(14+15)}\)
\(h = 11 \text{ }ft\)
So, the height of a room is 11 foot.
Example 4: Find the width of a container which is in the shape of a rectangular prism. If its surface area is 10300 square inches, length is 50 inches and height is 35 inches.
Solution:
\(l = 50\text{ }in\)
\(h = 35\text{ }in\)
\(SA = 10300\text{ }in^{2}\)
Rearrange the formula of SA for w
\(w = \frac{(SA-2 \times l \times h)}{2(h+l)}\)
\(w = \frac{(10300 -2 \times 50 \times 35)}{2(35+50)}\)
\(w = 40\text{ }in\)
So, the width of the container is 40 inches.
The sum total of the surface area of the rectangular faces of the prism is referred to as the surface area of a prism. There are two different kinds of it: lateral surface area and total surface area. In contrast to the lateral surface area (which only includes the lateral faces and excludes the base and top area), the total surface area of a rectangular prism refers to the sum total of area of all the six faces.
There are six faces in a rectangular prism.
When each of the dimensions of a rectangular prism is doubled, the surface area of the prism quadruples. That is, we get a surface area that is four times the original one.
There are eight vertices in a rectangular prism.