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)
To find the surface area of the figure, we need to calculate the surface area of each individual face and then add them together.
Surface area of rectangular prism:
- Front and back faces: 12 ft (length) * 8 ft (height) = 96 sq ft each
- Top and bottom faces: 12 ft (length) * 8 ft (width) = 96 sq ft each
- Left and right faces: 8 ft (height) * 8 ft (width) = 64 sq ft each
Total surface area of rectangular prism = 2(96) + 2(64) + 2(96) = 416 sq ft
Surface area of right triangular prism:
- Front face: 15 ft (hypotenuse) * 8 ft (width) / 2 = 60 sq ft
- Top face: 15 ft (hypotenuse) * h (height) / 2, where h is the height of the triangular prism
- Left face: 15 ft (hypotenuse) * h (height) / 2, where h is the height of the triangular prism
Total surface area of right triangular prism = 60 + h(15) + h(15)
Since the left side of the figure is 20 feet tall, the height of the right triangular prism must be 12 feet in order for the edges to align perfectly. Therefore, the total surface area of the figure is 416 sq ft + 60 + 12(15) + 12(15) = 616 sq ft.
So, the surface area of the figure is 616 square feet.