se 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)
To find the total surface area of the stand, we need to calculate the surface area of each pedestal and then add them together.
For pedestal 1:
Front and back faces: 20 inches x 15 inches x 2 = 600 square inches
Side faces: 20 inches x 11 inches x 2 = 440 square inches
Top face: 15 inches x 11 inches = 165 square inches
Total surface area of pedestal 1 = 600 + 440 + 165 = 1205 square inches
For pedestal 2:
Front and back faces: 20 inches x 11 inches x 2 = 440 square inches
Side faces: 20 inches x 7 inches x 2 = 280 square inches
Top face: 11 inches x 7 inches = 77 square inches
Total surface area of pedestal 2 = 440 + 280 + 77 = 797 square inches
For pedestal 3:
Front and back faces: 20 inches x 7 inches x 2 = 280 square inches
Side faces: 20 inches x 3 inches x 2 = 120 square inches
Top face: 7 inches x 3 inches = 21 square inches
Total surface area of pedestal 3 = 280 + 120 + 21 = 421 square inches
Now, add the surface areas of all three pedestals together to find the total surface area of the stand:
1205 + 797 + 421 = 2423 square inches
Therefore, the total surface area of the stand is 2423 square inches.