Surface Area Unit Test
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Question
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?
(1 point)
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:
- Area of the top and bottom: 2(12ft x 8ft) = 2(96ft^2) = 192ft^2
- Area of the front and back: 2(12ft x 8ft) = 2(96ft^2) = 192ft^2
- Area of the left and right sides: 2(8ft x 8ft) = 2(64ft^2) = 128ft^2
Total surface area of the rectangular prism = 192ft^2 + 192ft^2 + 128ft^2 = 512ft^2
Surface area of the right triangular prism:
- Area of the three rectangular sides: 2(15ft x 8ft) + 2(15ft x h) + 2(8ft x h) = 30ft x 8ft + 30ft x h + 16ft x h = 240ft^2 + 46ft x h
- Area of the two triangle ends: 2(1/2 x 8ft x 15ft) = 120ft^2
Total surface area of the right triangular prism = 240ft^2 + 120ft^2 + 46ft x h
The total height of the figure is 20ft, which is the sum of the height of the rectangular prism (8ft) and the height of the right triangular prism (h).
So, the surface area of the figure is 512ft^2 + 240ft^2 + 120ft^2 + 46ft x h.
Since we don't have the value of h, we cannot find the exact numerical value of the surface area without knowing the height of the right triangular prism.
the height is 12
Thank you for providing the height of the right triangular prism.
Given that the height of the right triangular prism is 12 feet, we can now calculate the surface area of the figure.
Surface area of the rectangular prism:
- Area of the top and bottom: 2(12ft x 8ft) = 2(96ft^2) = 192ft^2
- Area of the front and back: 2(12ft x 8ft) = 2(96ft^2) = 192ft^2
- Area of the left and right sides: 2(8ft x 8ft) = 2(64ft^2) = 128ft^2
Total surface area of the rectangular prism = 192ft^2 + 192ft^2 + 128ft^2 = 512ft^2
Surface area of the right triangular prism:
- Area of the three rectangular sides: 2(15ft x 8ft) + 2(15ft x 12ft) + 2(8ft x 12ft) = 240ft^2 + 360ft^2 + 192ft^2 = 792ft^2
- Area of the two triangle ends: 2(1/2 x 8ft x 15ft) = 120ft^2
Total surface area of the right triangular prism = 792ft^2 + 120ft^2 = 912ft^2
Therefore, the total surface area of the figure is 512ft^2 (rectangular prism) + 912ft^2 (right triangular prism) = 1424ft^2.
The surface area of the figure is 1424 square feet.