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)
The surface area of the figure can be calculated by finding the surface area of each individual prism and adding them together.
Surface area of the rectangular prism:
- Top and bottom faces: 2(12ft * 8ft) = 192 square feet
- Front and back faces: 2(8ft * 8ft) = 128 square feet
- Left and right faces: 2(12ft * 8ft) = 192 square feet
Total surface area of the rectangular prism = 192 + 128 + 192 = 512 square feet
Surface area of the right triangular prism:
- Front face: 8ft * 15ft = 120 square feet
- Right face: 8ft * 15ft = 120 square feet
- Left face (hidden): 8ft * height of the triangular prism
Total surface area of the right triangular prism: 240 + 8(height) square feet
Since the left face of the right triangular prism aligns perfectly with the top face of the rectangular prism, the surface area of this shared face must be deducted from the total surface area of the right triangular prism. This shared face area is:
- 8ft * 12ft = 96 square feet
So, the total surface area of the figure is:
512 square feet (rectangular prism) + 240 + 8(height) square feet (right triangular prism) - 96 square feet (shared face)
= 656 + 8(height) - 96 square feet
= 560 + 8(height) square feet
Therefore, the surface area of the figure is 560 + 8(height) square feet.