SOLUTION: Scott is making a special box to hold an irregularly shaped statue with a volume of 1757 in3 for mailing. The box is a right triangular prism. If the height of the box is 30 inches

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Question 769181: Scott is making a special box to hold an irregularly shaped statue with a volume of 1757 in3 for mailing. The box is a right triangular prism. If the height of the box is 30 inches while the sides of the bases are 12 inches, 16 inches, and 20 inches, how much packing material will fit around the statue?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a prism is the area of the base times the height.
The area of a triangle is base%2Aheight%2F2.
In a right triangle, one of the legs can be considered the base while taking the other leg as the height.
A triangle with sides measuring 12 inches, 16 inches, and 20 inches is a right triangle with legs measuring 12 inches and 16 inches, and a 20-inch hypotenuse.
12%5E2%2B16%5E2=20%5E2
(so you have some redundant information).
The area of such a triangle is
%2812in%29%2816in%29%2F2=96in%5E2
The volume of the box is %2896in%5E2%29%2830in%29=2880in%5E3
The volume of the packing material that will fit around the statue in that box is
2880in%5E3-1757in%5E3=1123in%5E3