To find the surface area of the rectangular prism, we first need to identify the dimensions given in the illustration. The prism is composed of six rectangles that contribute to its surface area.
From the prompt:
- The height (h) of the larger rectangles is given as 6 feet.
- The width (w) for both larger rectangles and the height for smaller rectangles is not explicitly mentioned, but we can deduce it:
- The smaller rectangles have a width of 3.5 feet (on the left side).
- The length (l) of the rectangle below (fourth rectangle) that shares the left side with the smaller rectangle is 8 feet.
Now we'll deduce the dimensions of the larger rectangles:
- The larger rectangles (at the top) both share a height of 6 feet
- Since all dimensions align logically, we can assume the base of the larger rectangles (the width) follows the smaller rectangles, which is the same width as the smaller ones.
For a clearer breakdown:
- Dimensions for larger rectangles:
- Height = 6 ft
- Width = 3.5 ft
- Dimensions for smaller rectangles:
- Height = 3.5 ft (to maintain proportion)
- Width = 8 ft
Now we calculate the areas of each rectangle:
-
Area of two larger rectangles (Front and Back): \[ 2 \times (6 \text{ ft} \times 8 \text{ ft}) = 2 \times 48 = 96 \text{ ft}^2 \]
-
Area of two smaller rectangles (Left and Right): \[ 2 \times (3.5 \text{ ft} \times 6 \text{ ft}) = 2 \times 21 = 42 \text{ ft}^2 \]
-
Top and Bottom rectangles (this could include the width fixed): \[ 2 \times (3.5 \text{ ft} \times 8 \text{ ft}) = 2 \times 28 = 56 \text{ ft}^2 \]
Now summing them all: \[ 96 \text{ ft}^2 + 42 \text{ ft}^2 + 56 \text{ ft}^2 = 194 \text{ ft}^2 \]
Thus, the total surface area of the prism is:
194 ft² (or 194 ft. squared).