use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a right triangular prism placed on top of a rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 feet and a height of 8 feet. The width of the rectangular prism is 8 feet. The edges of the hidden side face of the right triangular prism align perfectly with the edges of the hidden top face of the rectangular prism. The right triangular prism is aligned to the left of the rectangular prism. The height of the right triangular prism is not shown. The total height of the left side of the figure is 20 feet. The right triangular prism has a width of 8 feet. The hypotenuse side of the right triangular prism has a length of 15 feet.
what is the surface area of the figure?
__ft.^2
To find the surface area of the figure, we need to find the surface area of each individual shape and then add them together.
Surface area of the rectangular prism:
- Front and back faces: 8ft x 12ft = 96ft² (each face)
- Top and bottom faces: 12ft x 8ft = 96ft² (each face)
- Right and left faces: 8ft x 8ft = 64ft² (each face)
Total surface area of the rectangular prism: (96ft² + 96ft² + 64ft² + 64ft²) = 320ft²
Surface area of the right triangular prism:
- Front and back faces: (1/2)(8ft)(15ft) = 60ft² (each face)
- Right and left faces: 8ft x √(8^2 + 15^2) = 8ft x 17ft = 136ft² (each face)
- Top face: 12ft x 15ft = 180ft²
Total surface area of the right triangular prism: (60ft² + 60ft² + 136ft² + 136ft² + 180ft²) = 572ft²
Therefore, the surface area of the composite figure is:
320ft² (rectangular prism) + 572ft² (right triangular prism) = 892ft²
The surface area of the figure is 892 ft².
you sure?
Let's revisit our calculations:
Surface area of the rectangular prism:
- Front and back faces: 8ft x 12ft = 96ft² (each face)
- Top and bottom faces: 12ft x 8ft = 96ft² (each face)
- Right and left faces: 8ft x 8ft = 64ft² (each face)
Total surface area of the rectangular prism: (96ft² + 96ft² + 64ft² + 64ft²) = 320ft²
Surface area of the right triangular prism:
- Front and back faces: (1/2)(8ft)(15ft) = 60ft² (each face)
- Right and left faces: 8ft x √(8^2 + 15^2) = 8ft x 17ft = 136ft² (each face)
- Top face: 12ft x 15ft = 180ft²
Total surface area of the right triangular prism: (60ft² + 60ft² + 136ft² + 136ft² + 180ft²) = 572ft²
Therefore, the surface area of the composite figure is:
320ft² (rectangular prism) + 572ft² (right triangular prism) = 892ft²
The surface area of the figure is, indeed, 892 ft².
use the image to answer the 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?
__ft.^2
To find the surface area of the letter C sculpture, we need to find the surface area of the rectangular prism shape and then subtract the surface area of the removed portion.
Surface area of the rectangular prism shape:
- Front and back faces: 15ft x 10ft = 150ft² (each face)
- Top and bottom faces: 10ft x 1ft = 10ft² (each face)
- Left and right faces: 15ft x 1ft = 15ft² (each face)
Total surface area of the rectangular prism shape: (150ft² + 150ft² + 10ft² + 10ft² + 15ft² + 15ft²) = 350ft²
Surface area of the removed portion (rectangular piece):
- Front and back faces: 15ft x 7ft = 105ft² (each face)
- Top and bottom faces: 4ft x 7ft = 28ft² (each face)
- Side faces are removed
Total surface area of the removed portion: (105ft² + 105ft² + 28ft² + 28ft²) = 266ft²
Therefore, the surface area of the letter C sculpture is:
350ft² (full shape) - 266ft² (removed portion) = 84ft²
The surface area of the letter C sculpture is 84 ft².
you sure thats the answer?
Let's recalculate the surface area of the letter C sculpture:
Surface area of the rectangular prism shape:
- Front and back faces: 15ft x 10ft = 150ft² (each face)
- Top and bottom faces: 10ft x 1ft = 10ft² (each face)
- Left and right faces: 15ft x 1ft = 15ft² (each face)
Total surface area of the rectangular prism shape: (150ft² + 150ft² + 10ft² + 10ft² + 15ft² + 15ft²) = 350ft²
Surface area of the removed portion (rectangular piece):
- Front and back faces: 15ft x 7ft = 105ft² (each face)
- Top and bottom faces: 4ft x 7ft = 28ft² (each face)
- Side faces are removed
Total surface area of the removed portion: (105ft² + 105ft² + 28ft² + 28ft²) = 266ft²
Therefore, the correct surface area of the letter C sculpture is:
350ft² (full shape) - 266ft² (removed portion) = 84ft²
The correct surface area of the letter C sculpture is 84 ft².
is the answer 49 ft.^2?
Apologies for the confusion. Let's reexamine the calculations:
For the letter C sculpture, the surface area calculation should be as follows:
Surface area of the rectangular prism shape (whole letter C):
- Front and back faces: 15ft x 10ft = 150ft² (each face)
- Top and bottom faces: 10ft x 1ft = 10ft² (each face)
- Left and right faces: 15ft x 1ft = 15ft² (each face)
Total surface area of the rectangular prism shape: (150ft² + 150ft² + 10ft² + 10ft² + 15ft² + 15ft²) = 350ft²
Surface area of the removed portion (rectangular piece):
- Front and back faces: 15ft x 7ft = 105ft² (each face)
- Top and bottom faces: 4ft x 7ft = 28ft² (each face)
- Side faces are removed
Total surface area of the removed portion: (105ft² + 105ft² + 28ft² + 28ft²) = 266ft²
Therefore, the surface area of the letter C sculpture is:
350ft² (full shape) - 266ft² (removed portion) = 84ft²
So, the correct surface area of the letter C sculpture is 84 ft², not 49 ft². Thank you for your patience.