The surface area of the prism with the isosceles right triangle base is \(685ft^2\).

The surface area of any prism can be calculated using the following formula:

Let S= Surface Area

Let L= Lateral Area (Area of everything but the base)

Let B= Area of one base

Let P= Perimeter of the base

Let H= height of prism

\(S=L+2B\)

\(L=PH\)

Okay, let's get started now that we have determined the formula. Let's start by solving for L, the lateral surface area.

P= perimeter of the base

\(P= (11+11+15.6)ft=37.6ft\)

\(H=15ft\)

To find the lateral surface area, multiply P by h.

\(L=PH=37.6ft*15ft=564ft^2\)

The only variable to find next is B, the area of a triangle is 1/2*bh. Because the base is a right isosceles triangle, the base and the height are both 11.

\(B=\frac{1}{2}bh=\frac{1}{2}*11*11=60.5ft^2\)

Remember, the formula requires us to find 2B:

\(2B=(2*60.5)ft^2=121ft^2\)

Now, plug L and 2B back into the formula to get the final answer:

\(S=L+2B\)

\(S=(564+121)ft^2=685ft^2\)

Normally, you would have to find the surface area of the other triangular prism, but the final answer only asked about the triangle with the right isosceles base, so there is no need to calculate the other one.