To find the surface area of the figure, we need to calculate the surface area of each individual prism and then add them together.
Surface area of the rectangular prism:
2lw + 2lh + 2wh
= 2(12*8) + 2(12*8) + 2(8*8)
= 192 + 192 + 128
= 512 square feet
Surface area of the right triangular prism:
The surface area of a right triangular prism can be calculated by finding the area of the two triangular faces and the three rectangular faces, and then adding them together.
Area of the two triangular faces:
= 1/2 * base * height
= 1/2 * 8 * 15
= 60 square feet
Area of the three rectangular faces:
= perimeter of base * height
= (8 + 8 + 15) * h
= 31h square feet
Total surface area of the right triangular prism:
= 60 + 31h
Since the figures share a face, we don't count that shared face twice. So the total surface area of the figure would be the sum of the surface area of the rectangular prism and the total surface area of the right triangular prism minus the shared face:
512 + (60 + 31h) - 128
= 444 + 31h square feet
Therefore, the surface area of the figure is 444 + 31h square feet.
hey bot
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?
3 answers
are you 100% sure
I apologize for the oversight in my previous response. Let's correct the calculation for the surface area of the figure:
Surface area of the rectangular prism:
2lw + 2lh + 2wh
= 2(12*8) + 2(12*8) + 2(8*8)
= 192 + 192 + 128
= 512 square feet
Surface area of the right triangular prism:
The surface area of a right triangular prism can be calculated by finding the area of the two triangular faces and the three rectangular faces, and then adding them together.
Area of the two triangular faces:
= base * height
= 8 * 15
= 120 square feet
Area of the three rectangular faces:
= perimeter of base * height
= (8 + 8 + 15) * h
= 31h square feet
Total surface area of the right triangular prism:
= 120 + 31h
Since the figures share a face, we don't count that shared face twice. So the total surface area of the figure would be the sum of the surface area of the rectangular prism and the total surface area of the right triangular prism minus the shared face:
512 + (120 + 31h) - 128
= 504 + 31h square feet
Therefore, the corrected surface area of the figure is 504 + 31h square feet. Thank you for pointing that out.
Surface area of the rectangular prism:
2lw + 2lh + 2wh
= 2(12*8) + 2(12*8) + 2(8*8)
= 192 + 192 + 128
= 512 square feet
Surface area of the right triangular prism:
The surface area of a right triangular prism can be calculated by finding the area of the two triangular faces and the three rectangular faces, and then adding them together.
Area of the two triangular faces:
= base * height
= 8 * 15
= 120 square feet
Area of the three rectangular faces:
= perimeter of base * height
= (8 + 8 + 15) * h
= 31h square feet
Total surface area of the right triangular prism:
= 120 + 31h
Since the figures share a face, we don't count that shared face twice. So the total surface area of the figure would be the sum of the surface area of the rectangular prism and the total surface area of the right triangular prism minus the shared face:
512 + (120 + 31h) - 128
= 504 + 31h square feet
Therefore, the corrected surface area of the figure is 504 + 31h square feet. Thank you for pointing that out.
3 answers