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)
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:
- Two faces with dimensions 12ft x 8ft = 96 sq ft each
- Two faces with dimensions 8ft x 8ft = 64 sq ft each
- Two faces with dimensions 12ft x 8ft = 96 sq ft each
Total surface area of rectangular prism = 2(96) + 2(64) + 2(96) = 384 + 128 + 192 = 704 sq ft
Surface area of the right triangular prism:
The base of the right triangular prism is a right triangle with sides 8ft, 15ft, and 17ft (by Pythagorean theorem). The height is not given.
Area of the base = 1/2 x 8ft x 15ft = 60 sq ft
The lateral faces of the prism will be two isosceles triangles with base 15ft and height equal to the height of the prism.
Surface area of the right triangular prism = Area of the base + 2(area of lateral face)
= 60 + 2(15h) = 60 + 30h sq ft
Therefore, the total surface area of the figure = Surface area of rectangular prism + Surface area of right triangular prism
= 704 sq ft + 60 + 30h sq ft
The total surface area of the figure is 704 sq ft + 60 + 30h sq ft.