What is the Diagonal of a Rectangular Prism?
A rectangular prism is a 3-dimensional figure having a hollow internal space. It means that this shape is like a box that is used to fill some products from its inner side. But the overall shape of a rectangular prism is a little different from a box.
This type of prism has all angles of 90 degrees connecting its 6 faces with equal measures for opposite faces. Like other rectangular shapes, this figure can also be divided into two same sections by joining its opposite vertices.
The line that joins two opposite vertices of a rectangular prism in the lateral direction is called it's diagonal. In simple words, the diagonal of a rectangular prism is the line that joins the upper vertex of one face of a rectangular prism with the lower vertex of the opposite face.
It can also be drawn by joining the both lower or upper vertices of two opposite faces of a rectangular prism. In short, it is a lateral line that will join two corners or vertices of opposite faces of a prism. From this page, you will learn a lot about this length and the method to find it.
What is the diagonal height of a rectangular prism?
Undoubtedly, the diagonal of a rectangular prism can be drawn by joining two lower or upper corners. But it is also drawn by connecting two opposite corners of the faces that will set a height for a rectangular prism.
The diagonal height of a rectangular prism is the length of a vertical line drawn from the upper joining vertex of the diagonal. Normally, this length is equal to the height of a rectangular prism because the diagonal height will be perpendicular to that prism’s height.
Diagonal of a Rectangular Prism Formula
Like other terms related to a rectangular prism, we can also find the diagonal of a rectangular prism. For this purpose, we have to understand the formula used for this calculation.
Diagonal of a Rectangular Prism =√(l2 + w2 + h2) It means you only have to find the length, width, and height of a rectangular prism to find the length of a diagonal of a rectangular prism. You can easily find it by inserting the values in the above formula and calculating it through basic mathematical operations.
How to find the diagonal of a rectangular prism?
To explain the method to find the length of a diagonal of a rectangular prism, we have solved an example here.
example:
Find the diagonal of a rectangular prism if its length is 2m, width is 5m, and height is 7m.
Solution:
To find the length of the diagonal of such a rectangular prism, we have to put the values in the above formula.
Diagonal of a Rectangular Prism =√((2)2 + (5)2 + (7)2) m By solving the above equation, we found: Diagonal of a Rectangular Prism = 8.831 m
Conclusion
By checking the above example, you may have understood the way to find the diagonal of a rectangular prism in a simple method. If you are still confused and looking for some assistance, you can use a Rectangular Prism Calculator.
It is an online calculator that can show you different parameters related to a rectangular prism using its length, width, and height. Isn’t it good to use this calculator instead of struggling alone?
FAQ
How many diagonals does a rectangular prism have?
A rectangular prism can have a maximum of 4 diagonals.
How to find the diagonal height of a rectangular prism?
We can find the diagonal height of a rectangular prism by converting it into rectangular coordinates. It will help us in finding the height of this line by comparing it with the actual height of a prism.
What is the formula for the diagonal height of a rectangular prism?
There is no direct formula for the diagonal height of a rectangular prism. We can find the length of this line and then use different approaches to find its height.
What is the relationship between the diagonal of a rectangular prism and its volume?
No direct relationship is established between the diagonal of a rectangular prism and its volume because the diagonal is a length while the volume is a particular space covered by this figure.
What is the longest diagonal of a rectangular prism?
The longest diagonal of a rectangular prism is the diagonal connecting the upper corner of one face to the lower corner of the opposite face of the prism.
