To find the surface area of the figure, we first need to calculate the surface area of each individual shape (rectangular prism and right triangular prism) and then add them together.
For the rectangular prism:
- Front and back faces: 12 ft (length) * 8 ft (height) = 96 sq ft
- Top and bottom faces: 12 ft (length) * 8 ft (width) = 96 sq ft
- Left and right faces: 8 ft (height) * 8 ft (width) = 64 sq ft
Total surface area of the rectangular prism = 2(96) + 2(64) + 2(96) = 384 sq ft
For the right triangular prism:
- Front and back faces: 12 ft (length) * 8 ft (width) = 96 sq ft
- Bottom face (triangle): (1/2) * 12 ft * 15 ft = 90 sq ft
- Left and right faces: 15 ft (hypotenuse) * 8 ft (width) = 120 sq ft
Total surface area of the right triangular prism = 2(96) + 90 + 2(120) = 522 sq ft
Adding the surface area of the rectangular prism and the right triangular prism together, we get:
384 sq ft + 522 sq ft = 906 sq ft
Therefore, the total surface area of the composite figure is 906 square feet.
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