A special 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 Answer: the height of the box is: h = 13 inches
