A triangular prism has a triangle base with sides 8, 15, 17 units and height 20 units. Its total surface area is:

The base of the triangular prism is a triangle with side lengths 8 units, 15 units, and 17 units.

The height (length) of the prism is 20 units.

​$$\text{Area of triangle} = \frac{1}{2}\times \text{Base} \times \text{Height}$$​​

​$$\text{Lateral Surface Area} = \text{Perimeter of triangular base} \times \text{Height of prism}$$​​

​$$\text{Total Surface Area} = 2 \times \text{Area of triangular base} + \text{Lateral Surface Area}$$ 

Solution: 

As we can see that side length 8 unit, 15 unit and 17 unit is a triplet of right angle triangle 

So Hypotenuse = 17 unit, Base = 8 unit and Perpendicular = 15 unit 

Perimeter of triangle = 17 + 8 + 15 = 40 unit 

Area of triangle = $$\frac{1}{2} \times 8 \times 15 = 60 \, unit^2$$ 

Lateral Surface Area = $$40 \times20 = 800 \,unit^2$$ 

Total Surface Area = $$2 \times 60 + 800 = 920 \, unit^2$$ 

Thus, the Total Surface Area of Prism is 920 unit².​