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Let's take a glimpse of Egypt during 3000 BC. People were intelligent in their own way. In fact, one of their creation, which is the "Great Pyramid of Giza", is one of the wonders of the world. This is proof that Egyptians were amazing builders. But you are not here to learn about the Egyptians, you are here to learn about pyramids. The question is what is a pyramid? Let's talk about it.
What is a Pyramid
You might be thinking the origin of this shape came from Egyptians because they are well-known for their pyramids and we don't blame you for this. To be honest, this shape was first used by ancient Mesopotamia. This knowledge was passed through many civilizations and fortunately, we are also aware of pyramids. Take a look at the below image.
Yes, that is a pyramid. Let's analyze this three-dimensional shape. One thing is clear and that is it is a polyhedron. The second thing you see is its faces. The faces resemble the triangles but the base is different. The base looks like a hexagon and the hexagon is a polygon. However, we want you to note one thing and that is the base can change. This is up to the type of pyramid. That is why we want you to learn that the base will be a polygon. Let's conclude this shape, a pyramid is a polyhedron, whose base can be any polygon and whose lateral faces are triangles with a common vertex (apex of the pyramid). The height of the pyramid is the measure of the perpendicular line segment from the apex to the base. The apothem of a regular pyramid is the height of one of its lateral faces.
Unfold of a Pyramid
In the series of polyhedron, we include this topic because it is not only interesting but it is satisfying to the eyes as well. Under this heading, we will unfold the 3-dimensional pyramid shape to reveal its secrets. There are many types of pyramids, which one we are unfolding? The answer is the convex pyramid. Let's unfold it!
The above picture is the unfolded figure of a convex pyramid. We will use this information to find the formula for lateral and surface area of the pyramid.
Types of Pyramids
As mentioned before, there are different types of pyramids. We have listed them below with their description.
Regular Pyramid
Irregular Pyramid
The base of an irregular pyramid is an irregular polygon, and as a result, its faces are not equally sized.
Convex Pyramid
Concave Pyramid
Right Pyramid
Oblique Pyramid
Types of the Pyramids by their Base
The above types were generic types of pyramids, however, pyramids are also categorized according to their base. As mentioned before, pyramids have different bases and that is why they are further categorized according to their bases.
Triangular Pyramid
The base is a triangle.
Square Pyramid
Pentagonal Pyramid
Hexagonal Pyramid
Since you are aware of types of pyramids, take your time and tell us in the comments the type of pyramid is the "Great Pyramid of Giza"?
Calculation of the Apothem of a Pyramid
Calculation of the Lateral Edge of a Pyramid
Lateral Area of a Pyramid
The lateral area of a pyramid is the area of all faces of the pyramid neglecting the base face. Yes, it mean that you don't need to find the base area of the pyramid for finding lateral area.
Where,
perimeter of the base,
apothem of the pyramid.
Surface Area of a Pyramid
The surface area is the sum of all faces of the pyramid and this time, it includes the base too. Basically, you are finding the total space occupied by the boundary of the pyramid.
Volume of a Pyramid
The volume of a pyramid is the total space occupied by the total object. That includes the boundaries and the space entrapped inside of the pyramid.
Examples
Calculate the lateral area, surface area and volume of a square pyramid whose base edge is 10 cm and its height is 12 cm.
Calculate the lateral area, surface area and volume of a hexagonal pyramid whose base edge is 16 cm and its lateral edge is 28 cm.
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Interested learning more
Hello,
the solution of Exercise No.3 …volume 1 = 30m3
and the last fraction is 30/0.24 = 125