The problem describes a rectangular prism (cake) with a height of 4 inches and a base of 12 inches by 15 inches. We need to find the surface area of the sides and the top of the cake, which will have frosting.

1. Problem Description

The problem describes a rectangular prism (cake) with a height of 4 inches and a base of 12 inches by 15 inches. We need to find the surface area of the sides and the top of the cake, which will have frosting.

2. Solution Steps

First, we need to find the area of the top of the cake. This is a rectangle with sides 12 inches and 15 inches.

$Area_{top} = length * width = 12 * 15 = 180$ square inches.

Next, we need to find the area of the four sides of the rectangular prism.

The sides are rectangles.

Two sides have dimensions 4 inches by 12 inches, and the other two sides have dimensions 4 inches by 15 inches.

$Area_{side1} = height * length = 4 * 12 = 48$ square inches.

Since there are two such sides, the total area for these two sides is $2 * 48 = 96$ square inches.

$Area_{side2} = height * width = 4 * 15 = 60$ square inches.

Since there are two such sides, the total area for these two sides is $2 * 60 = 120$ square inches.

Now, we add the area of the top and the areas of the four sides to find the total surface area that will have frosting.

$Total Area = Area_{top} + Area_{side1} * 2 + Area_{side2} * 2$

$Total Area = 180 + 96 + 120 = 396$ square inches.

3. Final Answer

396