To find the surface area of the figure, we need to find the surface areas of both the rectangular prism and the right triangular prism, and then add them together.
Surface area of the rectangular prism:
- There are 2 rectangles with dimensions 12 ft x 8 ft (front and back faces).
- There are 2 rectangles with dimensions 8 ft x 8 ft (top and bottom faces).
- There are 2 rectangles with dimensions 12 ft x h (left and right side faces) where h is the height of the right triangular prism.
Surface area of the right triangular prism:
- There are 2 right triangles with base 8 ft, height h and hypotenuse 15 ft.
- There are 3 rectangles with dimensions 8 ft x h (front face), 15 ft x h (top face) and 15 ft x 8 ft (bottom face).
Surface area of the rectangular prism = 2(12 x 8) + 2(8 x 8) + 2(12 x h) = 192 + 128 + 24h = 320 + 24h
Surface area of the right triangular prism = 2(1/2 x 8 x h) + 3(8 x h + 15 x h + 15 x 8) = 8h + 72h + 120h = 200h
Total surface area = Surface area of rectangular prism + Surface area of right triangular prism
Total surface area = 320 + 24h + 200h
Total surface area = 320 + 224h
Since the height of the right prism is not given, we cannot calculate the exact surface area without it.
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 answer