To find the surface area of the rectangular prism in the shape of a letter "C", we will consider the outer surface area of the prism and the area of the cutout.
- Calculate the Surface Area of the Full Prism:
The overall dimensions of the prism are:
- Height (h) = 15 feet
- Width (w) = 10 feet
- Depth (d) = 1 foot
The surface area (SA) of a rectangular prism is given by the formula: \[ SA = 2(hw + hd + wd) \] Substituting the values into the formula: \[ SA = 2(15 \cdot 10 + 15 \cdot 1 + 10 \cdot 1) \] \[ SA = 2(150 + 15 + 10) = 2(175) = 350 \text{ ft}^2 \]
- Calculate the Area of the Cutout:
The cutout is a rectangular portion removed from the right center of the prism and has the following dimensions:
- Width = 7 feet
- Height = 15 feet
Thus, the area of the cutout is: \[ \text{Area of cutout} = \text{Width} \times \text{Height} = 7 \times 15 = 105 \text{ ft}^2 \]
- Adjust the Surface Area for the Cutout:
Since the cutout exposes an additional surface area corresponding to the inside of the cutout (since it removes the exterior), we need to add the surface area of the back wall of the cutout, which is:
- Width = 7 feet
- Depth = 1 foot
The area of the back wall of the cutout is: \[ \text{Area of back wall} = \text{Width} \times \text{Depth} = 7 \times 1 = 7 \text{ ft}^2 \]
- Calculate the Final Surface Area:
The final surface area of the letter "C" shape is: \[ \text{Final Surface Area} = \text{Surface Area of Full Prism} - \text{Area of Cutout} + \text{Area of Back Wall} \] \[ \text{Final Surface Area} = 350 - 105 + 7 = 252 \text{ ft}^2 \]
Thus, the surface area of the letter "C" is 252 square feet.