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
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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 Rectangular Prism:
- The two rectangle faces: 12 ft x 8 ft = 96 ft² (each)
- The two square faces: 8 ft x 8 ft = 64 ft² (each)
Total surface area of rectangular prism: 2(96 ft²) + 2(64 ft²) = 320 ft²
Surface Area of Right Triangular Prism:
- The rectangle face: 8 ft x 8 ft = 64 ft²
- The two triangular faces: (1/2)base x height = (1/2)(8 ft)(15 ft) + (1/2)(8 ft)(20 ft) = 60 ft² + 80 ft² = 140 ft²
Total surface area of right triangular prism: 140 ft² + 64 ft² = 204 ft²
Adding the surface areas of both shapes together:
320 ft² (rectangular prism) + 204 ft² (right triangular prism) = 524 ft²
Therefore, the surface area of the figure is 524 ft².