It's a pentagonal prism with a regular base, so the base is a regular pentagon 

and we can subdivide the base into 5 isosceles triangles, 

each with height 6 cm (the apothem of the base). 

Actually, let's subdivide each of those into two right triangles, 

so the area of the base is the area of 10 right triangles, 

each with an angle measuring 36 degrees 

(1/10 the full 360-degree circle around the center of the pentagon) 

and a side adjacent to that angle measuring 6 cm. 

To find the side opposite the 36-degree angle, we'll need trigonometry. 

(I hope that's what you're studying!) 

The tangent of the angle is the ratio of the side opposite to the side adjacent, 

so multiplying tan 36° by 6 cm will give us that side length, 

and the area of each right triangle is, of course, 

half the product of those two sides. 

We have 10 triangles, so the area of the base is 

10 × (6 cm) × [(tan 36°) × (6 cm)] / 2 

= 5 (tan 36°) (6 cm)^2 

Multiplying the area of the base by the height yields the volume: 

5 (tan 36°) (6 cm)^2 (10 cm) 

= 1800 (tan 36°) cubic cm 

= about 1307.78 cubic cm according to my calculator, 

which would round to 1308 cubic cm.