Use the image to answer the question.
An illustration shows three adjoining rectangular prisms placed together and labeled from the left as 2, 1, and 3. The length of the rectangular prisms along the front base is 20 inches for each. The depth of each adjoining prism is 20 inches. The height of the rectangular prism on the left labeled 2 is 11 inches; the height of the rectangular prism in the center labeled 1 is 15 inches; the height of the rectangular prism on the right labeled 3 is 7 inches.
At the Olympics, the winners of the gold, silver, and bronze medals stand on a tiered pedestal.
As labeled in the diagram, the height of pedestal 3 is 7 inches, the height of pedestal 2 is 11 inches, and the height of pedestal 1 is 15 inches. Assuming each pedestal is of equal width and depth, find the total surface area of the stand.
(1 point)
in.2
Skip to navigation
page 16 of 17
To find the total surface area of the stand, we need to calculate the surface area of each of the three rectangular prisms and then add them up.
Rectangular prism 2:
Front and back faces: 20 inches x 11 inches = 220 square inches
Top and bottom faces: 20 inches x 20 inches = 400 square inches
Side faces: 11 inches x 20 inches = 220 square inches (each, but there are two)
Total surface area for prism 2: 220 + 400 + 440 = 860 square inches
Rectangular prism 1:
Front and back faces: 20 inches x 15 inches = 300 square inches
Top and bottom faces: 20 inches x 20 inches = 400 square inches
Side faces: 15 inches x 20 inches = 300 square inches (each, but there are two)
Total surface area for prism 1: 300 + 400 + 600 = 1000 square inches
Rectangular prism 3:
Front and back faces: 20 inches x 7 inches = 140 square inches
Top and bottom faces: 20 inches x 20 inches = 400 square inches
Side faces: 7 inches x 20 inches = 140 square inches (each, but there are two)
Total surface area for prism 3: 140 + 400 + 280 = 820 square inches
Adding up the surface area of all three prisms:
860 + 1000 + 820 = 2680 square inches
Therefore, the total surface area of the stand is 2680 square inches.