Triangular Prism

A triangular prism is a prism whose bases are triangles and whose lateral faces are rectangles. It has 9 edges and 6 vertices.

Total Surface Area and Volume of Triangular Prism

The volume of a triangular prism can be found by multiplying the base times the height.

Because the triangle is right triangle,

a² = 3² + 4²

a² = 9+16

a² = 25

a = 5

So, the prism is:

The prism has two faces in dimension:

Area of each face = \(\frac{1}{2}\) x 3 x 4 = 6

Area of both faces = 6 + 6 = 12

It has one face of dimension:

Area = 5 x 6 = 30

It has one face of dimension

Area = 4 x 6 = 24

It has one face of dimension:

Area = 3 x 6 = 18

Total surface area of the sum of these:

Total surface area = 12+30+24=18 = 84

Now, lateral surface area = area of 3 rectangles

= 5 x 6 + 4 x 6 + 3 x 6

= (5 + 4 +3) x 6

= perimeter of triangular base x height of prism.

Thus, total surface area = lateral surface area + 2 x area of the triangular base

Also, volume of the triangular prism = area of base x height

Example:

Find the volume of the given triangular prism.

Solution:
Area of base (A) = area of ΔABC

= \(\frac{1}{2}\) x 4cm x 2cm

= 4cm²

Height of the prism (h) = 15 cm

Volume of prism (V) = A x h

= 4 x 15

= 60cm³