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)
ft.2
To find the surface area of the figure, we need to calculate the surface area of each individual shape and then add them together.
Surface area of the rectangular prism:
- Front and back faces: 12 feet * 8 feet * 2 = 192 square feet
- Top and bottom faces: 8 feet * 8 feet * 2 = 128 square feet
- Left and right faces: 12 feet * 20 feet * 2 = 480 square feet
Total surface area of the rectangular prism: 192 + 128 + 480 = 800 square feet
Surface area of the right triangular prism:
- There are 3 visible faces: the front, bottom, and side face.
- The front face area can be calculated as 1/2 * base * height = 1/2 * 8 feet * 15 feet = 60 square feet
- The bottom face area can be calculated as base * height = 8 feet * 15 feet = 120 square feet
- The side face area can be calculated using the Pythagorean theorem to find the height of the triangle: 8^2 + h^2 = 15^2
- Solving for h, we get h = √(15^2 - 8^2) = √(225 - 64) = √161 ≈ 12.69 feet
- The side face area can be calculated as 8 feet * 12.69 feet = 101.52 square feet
Total surface area of the right triangular prism: 60 + 120 + 101.52 = 281.52 square feet
Total surface area of the composite figure: 800 + 281.52 = 1081.52 square feet
Therefore, the surface area of the figure is 1081.52 square feet.