To find the surface area of the figure, we need to find the surface area of each individual shape (the rectangular prism and the right triangular prism) and then add them together.
Surface Area of Rectangular Prism:
- Front and back faces: 12 ft (length) * 8 ft (height) * 2 = 192 sq ft
- Top and bottom faces: 12 ft (length) * 8 ft (width) * 2 = 192 sq ft
- Left and right faces: 8 ft (width) * 8 ft (height) * 2 = 128 sq ft
Total surface area of rectangular prism = 192 + 192 + 128 = 512 sq ft
Surface Area of Right Triangular Prism:
- Front and back faces: 8 ft (width) * 12 ft (height) = 96 sq ft
- Left and right faces: 8 ft (width) * 15 ft (hypotenuse) / 2 = 60 sq ft
- Top face: 15 ft (hypotenuse) * 12 ft (height) / 2 = 90 sq ft
Total surface area of right triangular prism = 96 + 60 + 90 = 246 sq ft
Surface Area of the Figure:
Total surface area = Surface Area of Rectangular Prism + Surface Area of Right Triangular Prism
Total surface area = 512 sq ft + 246 sq ft = 758 sq ft
Therefore, the surface area of the figure is 758 square feet.
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 12. 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 answer
1 answer