Find the total surface area for the solid shown. (20 pts) with explanation ?

The surface area is simply the the sum of the areas of each face. We see that this triangular prism has three rectangles each with the same lengths, and two triangles, each with the same lengths. 

The dimensions of one such rectangle are 11.2 cm by 25.7 cm. We multiply these two dimensions to get the area: 

The dimensions of one such triangle are a base of 11.2 cm and a height of 9.7 cm. We multiply these dimensions together with one half to get: 

Remember, we have each rectangle three times, and each triangle twice. We multiply and add up to get the surface area: