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