Use the image to answer the question.

Question

An illustration shows a 3-dimensional vertical rectangular prism that appears as the letter upper C, with a rectangular portion removed from the right center. The rectangular prism is 15 feet high, 10 feet wide, and 1 foot deep. The width of the portion removed from the middle on the right side is 7 feet across. The height of the remaining two arms left at the top and bottom is 4 feet each.

In Los Cabos, Mexico, there is a big sculpture of block letters that welcomes you. The image shows the letter C
. What is its surface area?

(1 point)
sq ft

Answer 1

To calculate the surface area of the given 3-dimensional rectangular prism that resembles the letter "C," we first need to identify the exterior surfaces and then sum their areas.

1. Dimensions of the complete letter "C":

   • Height (h): 15 feet
   • Width (w): 10 feet
   • Depth (d): 1 foot

2. Removed rectangular section:

   • Width of removed section: 7 feet
   • Height of remaining arms (top and bottom): 4 feet each.

3. Surface area calculation:

   • The letter "C" essentially consists of four vertical rectangular sides and one top and one bottom.

   • Top and Bottom Surfaces:

     • For the top: There's a strip that goes from the left side to where it curves down, which is the width minus the removed width. So:
       • Top area = 3 ft (10 ft - 7 ft) * 1 ft = 3 sq ft
       • Bottom area = 3 ft (10 ft - 7 ft) * 1 ft = 3 sq ft

   • Vertical Sides (Surface areas):

     • Left side: Full height (15 ft) * depth (1 ft) = 15 sq ft
     • Right side (without the removed portion):
       • The height consists of two parts: the remaining arm (4 ft) + the full height minus the removed part (15 ft - 4 ft) = 15 ft.
       • So the right-side area (without removed part) = 15 ft * 1 ft = 15 sq ft.
     • Remaining sections:
       • Remaining arm on top = 4 ft (height) * 1 ft (depth) = 4 sq ft
       • Remaining arm on bottom = 4 ft (height) * 1 ft (depth) = 4 sq ft

4. Total Surface Area Calculation:

   • Total area = Top area + Bottom area + Left area + Right area + Top remaining arm area + Bottom remaining arm area
   • Total area = 3 + 3 + 15 + 15 + 4 + 4
   • Total area = 44 sq ft

Therefore, the surface area of the sculpture resembling the letter "C" is 44 sq ft.