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The figure represents a truncated prism. The base ABCD is a square, and the lateral edges AE, BF, CG, DH are perpendicular to the base. AB = 10 in., AE = 6 in., BF = 10 in., CG = 10 in., DH = 6 in. Find (a) the length of each face diagonal; (b) each face angle; (c) the length of each diagonal of solid; (d) the lateral area; (e) the total area; (f) the angle BFH; (g) the volume.
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| Photo by Math Principles in Everyday Life |
Solution:
(a) Label further the figure and draw a diagonal line at each face as follows
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| Photo by Math Principles in Everyday Life |
By Pythagorean Theorem, the length of the diagonals are
(b) Let's consider the side view of a truncated prism which is HDCG as follows
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| Photo by Math Principles in Everyday Life |
By using basic trigonometric functions, we can solve for the face angles as follows
The opposite side of a truncated prism which is AEFB, their face angles are also 68°11'55'' and 111°48'5''. The rest of the face angles are all 90°.
(c) Let's consider the given figure again and draw their diagonal lines as follows
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| Photo by Math Principles in Everyday Life |
The length of the diagonals of a truncated prism are
(d) The lateral area of a truncated prism is
(e) The total area of a truncated prism is
(f) Let's consider the given figure again as follows
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| Photo by Math Principles in Everyday Life |
By Cosine Law, the value of ∠BFH which is also α is
(g) The volume of a truncated prism is
