In this note, you will learn:

· What are pyramids?

. Volume and surface area of pyramids

· Application questions involving volume and surface area of pyramids

Today, we will be learning about pyramids. Pyramids exist all around us, from man-made architectures to everyday objects that we are used to seeing. So, without further ado, let’s begin!

## What are pyramids?

Based on geometrical terms, a pyramid is a polyhedron (a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices) formed by connecting a polygonal base and a point called the apex or vertex.

Note: A polygon is essentially a plane figure that is made up of a finite number of straight-line segments (at least three and above) connected to form a closed polygonal chain.

The number of straight-line segments is typically five or more, because we know that a three-sided polygon is called a triangle, and four-sided polygon is either called a rectangle or a square.

## How to find volume of pyramid?

The general formula to find the volume of a pyramid is:

### V = 1/3 l w h OR V = 1/3 X Base Area X Height

where V is the volume of the pyramid, l is the base length of the pyramid, w is the base width of the pyramid and h is the height of the pyramid

## How to find the surface area of pyramid?

The general formula to find the surface area of a pyramid is:

### Total Surface Area of pyramid = Sum of the area of each triangular face + Area of the polygonal base

## Application questions involving volume and surface area of pyramids

### How to find volume of a pyramid

OPQR is a triangular pyramid with a base area of 35 cm^2 and a height of 12 cm. Find the volume of the triangular pyramid.

Solution:

Volume of triangular pyramid = 1/3 X Base Area X Height

= 1/3 X 35 X 12

= 140 cm^3

### How to finding surface area of a pyramid

OJKLM is a pyramid with a square base of length 18 cm. Given that the slant height of the pyramid is 23 cm, find its total surface area.

Solution:

Area of each triangular face = 1/2 X 8 X 23

= 207 cm^2

Area of square base = 18 X 18

= 324 cm^2

Therefore, Total surface area of pyramid = 4 × area of each triangular face + area of square base

= 4 X 207 + 324

= 1152 cm^2

And that’s all for today, students! Math Lobby hopes that after this article, you have a clear understanding on these interesting geometrical shapes, their formulae and its application!

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