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 surface area of a rectangular prism is calculated using the formula: 2lw + 2lh + 2wh
- Plugging in the values: 2(12)(8) + 2(12)(8) + 2(8)(8) = 192 + 192 + 128 = 512 square feet
Surface area of right triangular prism:
- To find the surface area of a right triangular prism, we need to find the area of the three rectangular faces and the two triangular faces.
- The area of the triangular face can be calculated as 1/2 × base × height = 1/2 × 8 × 15 = 60 square feet
- The two rectangular faces have an area of 8 × 15 = 120 square feet each
- The total surface area of the right triangular prism is 2(120) + 60 = 300 square feet
Therefore, the total surface area of the figure is 512 + 300 = 812 square feet.
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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?
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