Surface Area Unit Test
12 of 1612 of 16 Items
Question
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 first need to find the surface area of each individual shape and then add them together.
Surface area of the rectangular prism:
- Front and back faces: 2(12 ft * 8 ft) = 192 sq ft
- Top and bottom faces: 2(12 ft * 8 ft) = 192 sq ft
- Left and right faces: 2(8 ft * 8 ft) = 128 sq ft
Total surface area of the rectangular prism = 192 + 192 + 128 = 512 sq ft
Surface area of the right triangular prism (not including the hypotenuse):
- Front and back faces: 2(8 ft * h) = 16h sq ft
- Left and right faces: 15 ft * h = 15h sq ft (since the hypotenuse is not visible)
- Top face: 8 ft * 15 ft = 120 sq ft
Total surface area of the right triangular prism = 16h + 15h + 120 = 31h + 120 sq ft
Therefore, the total surface area of the figure is 512 sq ft + 31h + 120 sq ft = 31h + 632 sq ft.