Square Pyramid
The name pyramid brings in our minds the images of the “Great Pyramids of Egypt”. The pyramids of Giza are from more than 2500 BC and are a perfect example of a square pyramid as they have a square base. A pyramid, as per its shape, is a monument or a structure, generally, it has a quadrilateral base. This base touches a triangular point. On the Giza plateau, these pyramids were said to bring the lonely structures that were touching the Sahara Desert. In Egypt, the count is said to be seventy as these were going up to the Nile River Valley. The next comes Mesopotamia that claimed to have used this shape for the first time using mud-brick structures that were called ziggurats. Further, these were used by Romans and Greeks. Followed by this, Pyramids had also been found in the Meroe kingdom in the Nubian, Maya cities within South and Central America and in China.
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
Pyramids are characterized by a unique geometric shape whose shape allows its weight to be distributed evenly across the structure. A pyramid is a shape that can fit all shapes inside of it (triangle, square, rectangle, etc.). In geometry, a pyramid is also called a polyhedron. It is made by connecting a polygon base (it is a 2-D shape with 3 or more straight sides) with an apex (a point at the top).
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
A pyramid can have a base of any shape; square, triangle, rectangle, and other shapes. The interesting thing about a pyramid is that each of its sides (each base edge and its apex) form a triangle.
What is a Square Pyramid
As discussed above, a pyramid can have a base of different shapes; the shape of its base gives the pyramid its name. So you can now figure out that Square pyramids are also polyhedra (more specifically, a pentahedron i.e. a polyhedron with 5 sides) like other pyramids with a square base. Details of a square pyramid face edges vertices are as follows:
It has five faces.
Four of its side faces are triangles.
It has five vertices or corner points.
It has eight edges.
Definition of a Square-based Pyramid
It is a three-dimensional (3D) geometrical figure with a square base and four triangular faces or sides that meet at the apex or a single point.
Equilateral square pyramid - If all the four triangular faces have the same edges, then such a square pyramid is termed an equilateral square pyramid
Right angle square pyramid - If the top point of the pyramid (apex) is right above the centre of its base such that a straight line from the apex cuts the base perpendicularly, then it is called a right angle square pyramid.
Formulas for a Square Pyramid
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
We have mentioned here some of the important formulas related to a square pyramid:
Surface of area = Base Area + \[\frac{1}{2}\] ∗ perimeter ∗ slant height = x\[^{2}\]+2x ∗ \[\sqrt{\frac{x^{2}}{4}+h^{2}}\]
Volume =\[\frac{1}{3}\]* base area * height = \[\frac{1}{3}\ast x^{2}\ast\] h
Slant height = \[\sqrt{h^{2}+\frac{x^{2}}{4}}\]
In the equation above: x = length of the side of the base square
h = height or altitude of the pyrami
Square Pyramid Net
A net diagram gives a flattened view of any solid shape by showing each face and base with all of their dimensions. The pyramid net of a square-based pyramid is its 2D faces laid out, that can be folded to create its 3D shape. You can imagine it as unfolding a pyramid and making it completely flat. The image below shows what it would look like. The four sides can be folded here to recreate the pyramid. A pyramid net helps you see each face of the pyramid with clarity. A square pyramid net is helpful in teaching 3D shapes in mathematics.
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
What are the Properties of a Square Pyramid?
The square pyramid properties are that it contains five faces. There are 4 side faces that are in a triangle shape. The base of this pyramid is square and it has corner points (having 5 vertices). The count of edges is 8 and the base of it is square. The prime aim of Vedantu mathematics subject specialists is that students are able to understand the topic from scratch as this subject demands to have the clarity of base. Without roots clarity, one cannot solve the simplest math equations. Therefore, Vedantu has explained the theory in a simplified manner and always encourages students to clear all their questions without any hesitation.
How to Draw a Square Pyramid?
Since pyramids are 3-D structures, they could be a little difficult to draw on paper. It requires accuracy of angles so that it looks like a 3-D shape on paper. Here we will look at the process of drawing a square pyramid step-wise. Let us first see what all we need to draw the pyramid
A ruler
A pencil
A rubber eraser
1. Step 1 - Choose the size of the pyramid you want to make, for this example let it be a square with side 5 cms.
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
2. Step 2 - Draw a 5 cm line at the base of the pyramid. Use your compass to measure from the point to the pencil at 5 cms.
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
3. Step 3 - Now put your compass at one end of the baseline and draw a circle. Repeat the same thing at the other end of the baseline. If this is done correctly then you should see both the lines crossing in the middle.
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
4. Step 4 - Connect the two ends from the baseline to the top so that you end up with a triangle as shown in the image below:
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
5. Step 5 - Now rub out the lines you drew in step 3.
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
6. Step 6 - To one side of this triangle, draw an extension making sure the baseline of that side is above the first baseline you drew. You can get clarity with the image below:
(Image will be Uploaded Soon)
(Image will be Uploaded Soon)
7. Your square pyramid is ready on paper.
(Image will be Uploaded Soon)
FAQs on Square Pyramid – Definition, Formulas and How to Draw A Square Pyramid
1. What is Johnson's Solid
In a square-based pyramid, if all of its triangular sides are equilateral, i.e., all the sides and angles of the triangles are equal, then all the edges of the square pyramid will also be equal. This is called a Jhonson’s solid, which in geometry is a convex polyhedron. The name is given by Norman Jhonson, who published a list of 92 such solids in 1966. Johnson’s solid applies to other geometric figures provided they are convex polyhedrons that are not uniform but have regular polygon faces.
2. Apart from Square Pyramids, What are the Other Types of Pyramids and their Features?
The other types of pyramids apart from the square pyramid are:
Triangular Pyramids - Triangular pyramids have a triangular base as well as triangular faces. Its key features are:
It has 4 faces.
Three of the side faces are triangles.
It has a triangular base.
It has 4 vertices or common points.
It has 6 edges.
It is a tetrahedron.
(Image will be Uploaded Soon)
Pentagonal Pyramids - A pentagonal pyramid has a pentagonal base and triangular faces. Its key properties are:
It has 6 faces.
Its 5 side faces are triangular in shape
Its base is a pentagon.
It has 6 vertices or corner points.
It has 10 edges.
(Image will be Uploaded Soon)
3. Differentiate between the right pyramid and the oblique pyramid and regular pyramid and irregular pyramid
The difference between these two can be explained as below:
The position of the apex in a pyramid makes it either a right or an oblique pyramid. In the right pyramid, the apex or top point is directly above the base, while in an oblique pyramid, it is not.
(Image will be Uploaded Soon)
The shape of the base is the differentiating factor between a regular and an irregular pyramid. If the base of a pyramid is a regular polygon, it makes a regular pyramid; otherwise, it is an irregular pyramid.
(Image will be Uploaded Soon)
4. How can I draw a pyramid?
Due to having a 3-D structure, it may be a bit tough to draw them on paper. This will need accuracy while drawing angles to provide them proper 3-D shape on the paper. To draw a pyramid, you need to have a pencil, an eraser, and a ruler. First of all, you are supposed to select the size of a pyramid that you want to draw. Draw it according to the measurement that you thought of. Now, you need to use a compass to draw a circle. If it is completed correctly, you can check both of the lines that they are perfectly crossing in the middle. Finally, you can connect these ends using the baseline and it is ready for you.
