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?
To find the surface area of the composite figure, we need to calculate the surface areas of the individual prisms and then add them together.
Surface area of rectangular prism:
- Front and back faces: 12 feet x 8 feet = 96 square feet
- Top and bottom faces: 12 feet x 8 feet = 96 square feet
- Left and right faces: 8 feet x 8 feet = 64 square feet
Total surface area of rectangular prism: 96 + 96 + 64 = 256 square feet
Surface area of right triangular prism:
- Front and back faces: 12 feet x 15 feet/2 = 90 square feet
- Left and right faces: 15 feet x 8 feet = 120 square feet
- Bottom face (base of the triangle): 8 feet x 15 feet = 120 square feet
Total surface area of right triangular prism: 90 + 120 + 120 = 330 square feet
Total surface area of the composite figure: 256 (rectangular prism) + 330 (right triangular prism) = 586 square feet
Therefore, the surface area of the figure is 586 square feet.