Volume of Equilateral Triangle

Introduction

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. They are regular polygons, and can therefore also be referred to as regular triangles.As, equilateral triangle is two dimensional, it is impossible to determine its volume.So, lets know how to determine volume of the prism with equilateral triangular base.

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Formula for Volume of Equilateral Triangle Base Prism:

The volume of equilateral triangle, ` v = 1/3 B xx H`

Example for Volume of Equilateral Triangle Base :

Example 1. Find the volume of equilateral triangle base prism of side 10 cm and height `17/2 cm`

Solution:

Let, H = `17/2 cm` , B = 10cm

Formula used:  ` V = 1/3 B H`

Therefore, volume of equilateral triangle base prism ,

`V = 1/3 xx 10 xx 17/2` = `85/3 cm3`

Example2. Find the volume of equilateral triangle base prism of side 100 m and height 85 m

Solution:

Let, `H = 17/2 m` , B = 10 m

Formula used: ` V = 1/3 B H`

Therefore, volume of equilateral triangle base prism,

`V = 1/3 xx 10 xx 17/2`

= 2833.33 m3

Example3. Find the volume of equilateral triangle base prism of side 9 cm and height `15/2` cm

Solution:

Let, `H = 15/2 cm` , B = 9 cm

Formula used:   `V = 1/3 B H`

Therefore, volume of equilateral triangle base prism ,

`V = 1/3 xx 9 xx 15/2`

= `45/2` cm3

Example4. Find the volume of equilateral triangle base prism of side 90 cm and height 75 cm

Solution:

Let, H = 75cm, B = 90 cm

Formula used:      `V = 1/3 B H`

Therefore, volume of equilateral triangle base prism ,

`V = 1/3 xx 90 xx 75`

= 2250 cm3



Practice Problems Volume of Equilateral Triangle Base Prism

1. Find the volume of equilateral triangle base prism of side 180 m and height 156 m

2. Find the volume of equilateral triangle base prism of side 450 cm and height 390 cm

Solution for practice problems of volume of equilateral triangle base prism :

1. 9360 m3

2. 58500cm3