Aspecial box designed to hold an antique artifact is shaped like a triangular prism. the surface area of the box is 421.2 square inches. the height of the base triangle is 7.8 inches and each side of the base triangle is 9 inches long. what is the height of the box?

The area of the base is:
 A = root ((s-a) * (s-b) * (s-c) * (s))
 Where,
 a, b, c: sides of the triangle
 s = (a + b + c) / 2
 We have then:
 s = (9 + 9 + 9) / 2
 s = 13.5
 A = root ((13.5-9) * (13.5-9) * (13.5-9) * (13.5))
 A = 35.07
 Then, the surface area of the prism is:
 S.A = 2 * A + 9h + 9h + 9h
 Where,
 h: height of the prism:
 Substituting values:
 421.2 = 2 * (35.07) + 9h + 9h + 9h
 Clearing h:
 27h = (421.2 - 2 * (35.07))
 h = (421.2 - 2 * (35.07)) / (27)
 h = 13
 
 the height of the box is:
 h = 13 inches

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