Respuesta :

Step-by-step explanation:

The volume of a prism is:

V = AH

where A is the area of the base and H is the height.

The base is a triangle, so the area is:

A = 1/2 b h

We know that b = 3.  To find h, we can split the triangle in half.  Then we can either use Pythagorean theorem to find h, or properties of a 30-60-90 triangle.

The short leg is 3/2, so the height is 3/2 √3.

A = 1/2 (3) (3/2 √3)

A = 9/4 √3

Therefore:

V = (9/4 √3) (6)

V = 27/2 √3