To find the surface area of the figure, we need to find the surface area of each individual shape and then add them together.
Surface area of the rectangular prism:
- 2(length * width) + 2(width * height) + 2(length * height)
- 2(12*8) + 2(8*8) + 2(12*8) = 192 + 128 + 192 = 512
Surface area of the right triangular prism:
- To find the surface area of a right triangular prism, we need to find the areas of the three rectangular faces and two triangular faces.
- The triangular faces each have a base of 8 feet and a height of 15 feet, making the area of each triangular face 0.5 * 8 * 15 = 60 square feet. Since there are two triangular faces, the total area for the triangular faces is 120 square feet.
- The rectangular faces have a base of 8 feet and a height of 20 feet for the left face of the right triangular prism. The area of the left face is 8 * 20 = 160 square feet. Since there are two rectangular faces, the total area for the rectangular faces is 320 square feet.
- Adding the areas of the two types of faces together, we get a total surface area of 120 + 320 = 440 square feet.
Therefore, the total surface area of the figure is 512 (rectangular prism) + 440 (right triangular prism) = 952 square feet.
Surface Area Unit Test
12 of 1612 of 16 Items
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