The surface area of a triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces. Let's calculate the area of the triangular bases and the area of the rectangular faces one at a time. Then we can add them together.
Triangular Bases
The bases have a length of 8 inches and a height of 6 inches. The area of a triangle is half the product of a length and the height. Let's use this fact to find the area of a single base of our prism.
1/2( 8)( 6) = 24
The area of one triangular base is about 24 square inches. Because both of the triangular bases are exactly the same, we know that the area of the second triangular base is 24 square inches as well. Let's add them together!
Area of the Triangular Bases
24 + 24 = 48in^2
Rectangular Faces
We do not know the height of the prism which acts a width of the rectangular faces. We will call this missing height h. However, we know the sides of the triangle, so we know the lengths of the rectangular faces. They are: 8, 6, and 10 inches. The area of a rectangle is a product of its length and width. Let's use this fact to write the sum of areas of the rectangular faces.
8 h + 6 h + 10 h = 24h
Surface Area of the Prism
Now, we know that the surface area of 228 square inches. The surface area of a prism is also a sum of areas of bases and the rectangular faces. We can use this fact to write the following equation.
228 = 48 + 24h
Finally, let's solve this equation to find h, the height of the prism.
