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 go on answer
The surface area of the figure can be calculated by finding the surface area of each individual face and adding them together.
Surface area of rectangular prism = 2lw + 2lh + 2wh
= 2(12)(8) + 2(12)(8) + 2(8)(8)
= 192 + 192 + 128
= 512 ft^2
Surface area of triangular prism = base area + lateral area
= 1/2 * base * height + perimeter of base * height
= 1/2 * 8 * 15 + (8 + 15 + 17) * h
= 60 + 40h
Total surface area = 512 + (60 + 40h)
= 572 + 40h ft^2
Therefore, the surface area of the figure is 572 + 40h square feet.
tell me what that equation you said means.
The equation I provided was breaking down the surface area calculation into two parts: the surface area of the rectangular prism and the surface area of the triangular prism.
For the rectangular prism:
- The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.
- We plug in the values provided in the illustration (l=12, w=8, h=8) into the formula to calculate the surface area of the rectangular prism.
For the triangular prism:
- The total surface area of a triangular prism involves calculating the base area (1/2 * base length * height) and the lateral area (perimeter of the base * height).
- We use the given values for the triangular prism (base length = 8, height = unknown, hypotenuse = 15) to calculate the base area and perimeter, and then combine them to find the total surface area of the triangular prism.
By adding the surface areas of the rectangular prism and the triangular prism together, we can find the total surface area of the composite figure.