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
Yes, the surface area of the figure is 45h + 632 square feet. Without knowing the height of the right triangular prism, we cannot calculate the exact surface area value.
To find the surface area of the figure, you need to calculate the surface area of each individual prism and then add them together.
Surface area of rectangular prism = 2lw + 2lh + 2wh
= 2(8)(8) + 2(8)(12) + 2(8)(12)
= 128 + 192 + 192
= 512 square feet
Now, calculate the surface area of the right triangular prism. The lateral surface area of a right triangular prism is equal to the perimeter of the base times the height of the prism, plus the area of the two triangular bases.
Lateral surface area = perimeter of base x height + 2 x base area
= 15 + 15 + 15 + h (+ 2(1/2)(8)(15))
= 45h + 120
Now add the lateral area to the rectangular prism area.
Total surface area = lateral surface area of triangular prism + surface area of rectangular prism
= 45h + 120 + 512
= 45h + 632
Therefore, the surface area of the figure is 45h + 632 square feet.