Determine the surface area of the rectangular prism with given dimensions.

Steps to Solve

1. Visualize the Rectangular Prism Pattern

Imagine a rectangular prism unfolded into a net. From the description, we know the following: It is a stack of 4 rectangles. The length of these rectangles is 36 inches. The width of the last rectangle is 18 inches. Two squares (18 inches x 18 inches) are attached to each side of the second rectangle in the stack.

2. Determine the Dimensions

The length of the rectangle is given as 36 inches. The width of the base rectangle is given as 18 inches. From this, we deduce that the width/height of the prism is also 18 inches.

3. Identify the Faces and their Areas

A rectangular prism has six faces. Let's denote the length $l$, width $w$, and height $h$ of the prism as $l = 36$ inches, $w = 18$ inches, and $h = 18$ inches.

• Two faces have dimensions $l \times w = 36 \times 18$.
• Two faces have dimensions $l \times h = 36 \times 18$.
• Two faces have dimensions $w \times h = 18 \times 18$.

4. Calculate the Area of Each Type of Face

• Area of the $36 \times 18$ rectangles: $36 \times 18 = 648$ square inches.
• Area of the $18 \times 18$ squares: $18 \times 18 = 324$ square inches.

5. Calculate the Total Surface Area

The surface area is the sum of the areas of all six faces:

$$SA = 2(l \times w) + 2(l \times h) + 2(w \times h)$$

$$SA = 2(36 \times 18) + 2(36 \times 18) + 2(18 \times 18)$$

$$SA = 2(648) + 2(648) + 2(324)$$

$$SA = 1296 + 1296 + 648$$

$$SA = 3240$$