Here in this article we will be discussing about the triangle prism. In geometry an n-sided prism is defined as a shape with a n-sided polygon as base on two sides connected by n-number of faces. The bases will have equal number of sides with equal side lengths. The distance between the two bases is called as the height of the prism. For a triangular prism there will be three sided base on both sides connected by three faces.

As described before the two bases of the prism will be triangles connected by three faces.

The distance between the two faces is called as the height of the triangular prism.

Basically the volume of the triangular prism is calculated by multiplying the height of the prism with the base area. The measurement of base area can be taken from any two sides since both the sides will have the same area.

The formula for calculating the volume of the triangular prism with side length s and height of the prism h is,

Volume = √3 hs^{2}/4

The surface area is the sum of the areas of the two bases and the area of the three faces of the prism. The formula for calculating the surface area of the triangular prism is,

Surface area = √3 s^{2}/2 + 3sh

1. The height of the given prism is 7cm and the side length is 3cm. Find the volume and the surface area of the triangle prism.

Solution: **surface area = 2√3 s ^{2}/4 + 3sh**

= 2√3 32/4 + 3x3x7

= 9√3/2 + 9x7

= 63+ 7.79

= 72.79 cm^{2}

**Volume = √3hs ^{2}/4**

= √3 63/4

=15.75√3

= 27.28 cm^{3}

2. For a triangle prism with a side length of 2.5cm and height of 10cm. calculate the area and the volume of the prism.

**Solution:**

**Surface area = 2√3 s ^{2}/4 + 3sh**

= 2√3 (2.5)^{2}/4 + 3x2.5x10

= 6.25√3/2 + 25x3

= 5.41+ 75

= 79.41 cm^{2}

**Volume = √3hs ^{2}/4**

= 10√3 (2.5)^{3}/4

= 10√3 (15.625)/4

= 67.65 cm^{3}

1. The perimeter of the given triangle prism base is 12cm and the height of the prism is 6cm. Find the prism volume and surface area.

**Answer: Volume = 69.28 cm ^{3} ; Surface area = 133.85 cm^{2}**

2. The side length of the given triangle prism is 5 cm and the height is 12cm. Find the volume of the triangle prism.

**Answer: Volume = 129.9 cm ^{3}**