Square Pyramid – Definition, Formulas and How to Draw A 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.

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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).

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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

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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.

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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.

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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.

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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.

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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:

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5. Step 5 - Now rub out the lines you drew in step 3.

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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:

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7. Your square pyramid is ready on paper.

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