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
To find the surface area of the figure, we need to calculate the surface area of the rectangular prism and the surface areas of the two triangular faces of the right triangular prism.
Surface area of rectangular prism = 2lw + 2lh + 2wh
= 2(12)(8) + 2(12)(8) + 2(8)(8)
= 192 + 192 + 128
= 512 square feet
Surface area of each triangular face of the right triangular prism = 0.5 * base * height
= 0.5 * 8 * 15
= 60 square feet (for each face)
Since there are two triangular faces, the total surface area of the figure is:
512 + 60 + 60 = 632 square feet
So, the surface area of the figure is 632 square feet.
are you sure?
I apologize for the error in my previous response. Let's correct it:
Surface area of the rectangular prism = 2lw + 2lh + 2wh
= 2(12)(8) + 2(12)(8) + 2(8)(8)
= 192 + 192 + 128
= 512 square feet
The right triangular prism has 2 triangular faces and 3 rectangular faces (1 base and 2 lateral faces).
Surface area of each triangular face of the right triangular prism = 0.5 * base * height
= 0.5 * 8 * 15
= 60 square feet (for each face)
Surface area of the rectangular faces of the right triangular prism = lw
= 8 * 15
= 120 square feet (for each face)
Total surface area of the right triangular prism = 2(60) + 3(120)
= 120 + 360
= 480 square feet
Total surface area of the figure = surface area of the rectangular prism + surface area of the right triangular prism
= 512 + 480
= 992 square feet
Therefore, the correct surface area of the figure is 992 square feet. Thank you for pointing out the mistake.
try again your answer is wrong. please answer the question accurately
I apologize for the previous errors. Let's try again to calculate the surface area of the figure accurately.
Surface area of the rectangular prism = 2lw + 2lh + 2wh
= 2(12*8) + 2(12*8) + 2(8*8)
= 192 + 192 + 128
= 512 square feet
The right triangular prism has 2 triangular faces and 3 rectangular faces (1 base and 2 lateral faces).
Surface area of each triangular face of the right triangular prism = 0.5 * base * height
= 0.5 * 8 * 15
= 60 square feet (for each face)
Surface area of the rectangular faces of the right triangular prism = lw
= 8 * 15
= 120 square feet (for each face)
Total surface area of the right triangular prism = 2(60) + 3(120)
= 120 + 360
= 480 square feet
Total surface area of the figure = surface area of the rectangular prism + surface area of the right triangular prism
= 512 + 480
= 992 square feet
Therefore, the surface area of the figure is 992 square feet. Thank you for pointing out the previous mistakes.