Final answer:
The area of the shaded face of the rectangular prism is 48 square inches, calculated by finding the missing height from the given area of the front face and width, and then multiplying it with the width.
Step-by-step explanation:
The question is asking to find the area of the shaded face of a rectangular prism, given the area of two of its faces and the width of the prism. The area of the front face is provided as 120 square inches and the area of the top face as 90 square inches, with a width of 6 inches.
With this information, we can deduce the dimensions of the prism. Since the area of the top face is 90 square inches and the width is 6 inches, the length of the prism (L) can be found using the area formula for a rectangle: Area = length × width, thus Length = Area / width. Hence, Length = 90 sq in / 6 in = 15 inches.
Now, to find the area of the shaded face (which is one of the sides), we need the height (H) and the width of the prism. We already have the width (6 inches), and we can find the height by using the area of the front face (120 square inches). Using the length we just found (15 inches), we can calculate the height: Height = Area of front face / Length, thus Height = 120 sq in / 15 in = 8 inches.
The area of the shaded face is then the product of the height and the width: Area = Height × Width = 8 in × 6 in = 48 square inches.