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The figure above shows a solid with thickness of 1, a square
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15 May 2020, 11:53
15 May 2020, 11:53
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23% (02:07) correct
76% (01:44) wrong based on 126 sessions
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The figure above shows a solid with thickness of 1, a square base and a square top, and 4 identical trapezoids as side surfaces. What is the surface area of the solid?
Consider all that apply
A. 38
B. 50
C. \(34 \sqrt{2}\)
D. \(34+4 \sqrt{2}
\)
E. \(34+16 \sqrt{2}\)
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#greprepclub The figure above shows a solid with thickness.jpg [ 16.88 KiB | Viewed 5349 times ]
Re: The figure above shows a solid with thickness of 1, a square
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15 May 2020, 14:37
15 May 2020, 14:37
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area of top square = 3*3 = 9
area of bottom square = 5*5 = 25
area of trapezoid = 1/2(sum of parallel sides) * distance between them
distance between parallel side can be calculated from triangle abc:
ab = 1 (depth of solid), bc = 1 (1/2(length of bottom square-length of top square)) by right angle triangle ac = √2
area of a trapezoid = 1/2 (3+5) * √2 = 4√2
there are four such trapezoids in fig = 4*4√2 = 16√2
the surface area of solid = 9 + 25 + 16√2 = 34 + 16√2
area of bottom square = 5*5 = 25
area of trapezoid = 1/2(sum of parallel sides) * distance between them
distance between parallel side can be calculated from triangle abc:
ab = 1 (depth of solid), bc = 1 (1/2(length of bottom square-length of top square)) by right angle triangle ac = √2
area of a trapezoid = 1/2 (3+5) * √2 = 4√2
there are four such trapezoids in fig = 4*4√2 = 16√2
the surface area of solid = 9 + 25 + 16√2 = 34 + 16√2
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#greprepclub The figure above shows a solid with thickness.jpg [ 12.41 KiB | Viewed 4404 times ]
General Discussion
Re: The figure above shows a solid with thickness of 1, a square
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15 May 2020, 11:53
15 May 2020, 11:53
Expert Reply
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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