To find the surface area of the figure, we first need to calculate the surface area of each individual shape and then add them together.
Surface area of the rectangular prism:
- Front and back faces: 12 feet * 8 feet = 96 ft² (two identical faces)
- Top and bottom faces: 12 feet * 8 feet = 96 ft² (two identical faces)
- Left and right side faces: 8 feet * 8 feet = 64 ft² (two identical faces)
Total surface area of the rectangular prism: 96 ft² + 96 ft² + 64 ft² = 256 ft²
Surface area of the triangular prism:
- Front and back faces: 8 feet * 20 feet = 160 ft² (two identical faces)
- Two triangular faces: (1/2) * 8 feet * 15 feet = 60 ft² (one triangular face)
Total surface area of the triangular prism: 160 ft² + 160 ft² + 60 ft² = 380 ft²
Therefore, the total surface area of the composite figure is:
256 ft² + 380 ft² = 636 ft²
Answer: 636 ft²
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 point)
ft.2
1 answer