What is a Rectangular Pyramid?
A rectangular pyramid is a solid with a rectangle-shaped base and triangular lateral faces. The base of a rectangular pyramid is rectangular, but the lateral faces are triangular. The sides of a pyramid are usually triangular, but the base can be a square or hexagonal in shape. The base, face, edges, and vertices are the distinguishing features of all of these types of pyramids. The properties and formulae of a rectangular pyramid are unique. The shape of a rectangular pyramid is depicted in the image.
Faces, Vertices and Edges
Let’s take a look at the properties of the faces, edges and vertices of a rectangular pyramid.
Faces: A rectangular pyramid has five faces. It has one rectangular base and four triangular faces at its sides. The opposite triangular faces are identical.
Vertices: The points where the edges meet or intersect are known as vertices. In a rectangular pyramid, there are five vertices. The apex of the pyramid is the common vertex at which the triangular faces of the pyramid meet.
The remaining four vertices can be found at the corners of the rectangular base.
Edges: The intersection of two faces or surfaces creates each edge of the rectangular pyramid. Hence this type of pyramid has eight edges. The rectangular base has four of the eight edges, while the other four edges meet at the apex.
Rectangular Pyramid Formula
Here is the formula for calculating the surface area and volume of a rectangular pyramid:
A rectangular pyramid’s surface area is = Base area + Area of lateral faces
A rectangular pyramid’s volume is calculated as follows:
\(V~=~\frac{1}{3}~(l~\times~w~\times~h) \)
Where,
\(l \) = length of the rectangular base.
\(w\) = width of the rectangular base.
\(h \) = height of the pyramid.
Solved Rectangular Pyramid Examples
Example 1: Find the surface area of the square pyramid in the image.
Solution:
We can use the help of a net of a rectangle pyramid to find the area of each face.
Base area \(=~8~\times~8~=~64~m^2 \)
Since, there are four lateral faces.
Therefor, the area of the 4 lateral faces\(~=~4~\times~\frac{1}{2}~\times~8~\times~12~=~192~m^2\)
Hence, surface area of the square pyramid\(~=64~+~192~=~256~m^2\)
Example 2:
What is the volume of a regular rectangular pyramid with a height of 20 inches and a rectangular base of length 12 inches and width 10 inches ?
Solution:
The volume of a rectangular pyramid is calculated by the following formula:
\(V~=~\frac{1}{3}~(l~\times~w~\times~h) \)
It is given that,
\(l \) = 12 inches
\(w \) = 10 inches
\(h\) = 20 inches
\(V~=~\frac{1}{3}~\times~12~\times~10~\times~20 \)
\(~=~800~in^3 \)
As a result, the given rectangular pyramid has a volume of 800 cubic inches.
Example 3:
Calculate the volume of the pyramid in the diagram below:
Solution:
It is given that the length of the rectangular base is 8, the width of the rectangular base is 6, and the height of the pyramid is 9.
The volume of a pyramid is calculated by the following formula:
\(V~=~\frac{1}{3}~(l~\times~w~\times~h) \)
\(V~=~\frac{1}{3}~\times~8~\times~6~\times~9 \)
\(~=144\) cubic units.
As a result, the given rectangular pyramid has a volume of 144 cubic units.
The volume (V) of a pyramid can be calculated easily using the formula \(V~=~\frac{1}{3}~\times~\text{Base Area}~\times~\text{Height} \).
A net of a solid is what it looks like if the solid was opened out and laid flat on a surface. The net of a rectangular pyramid is made up of four triangular faces and a rectangular base.
There are two types of rectangular pyramids:
- Right rectangular pyramid: A right rectangular pyramid is one in which the apex of the rectangular pyramid is directly above the center of the base.
- Oblique rectangular pyramid: An oblique rectangular pyramid is one in which the apex of the rectangular pyramid is not directly above the center of the base.