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The figure above shows a solid with thickness of 1, a square

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Carcass
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The figure above shows a solid with thickness of 1, a square [#permalink] New post   15 May 2020, 11:53
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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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Re: The figure above shows a solid with thickness of 1, a square [#permalink] New post   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
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Re: The figure above shows a solid with thickness of 1, a square [#permalink] New post   15 May 2020, 11:53
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Re: The figure above shows a solid with thickness of 1, a square [#permalink] New post   15 May 2020, 15:19
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Great job :)
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Re: The figure above shows a solid with thickness of 1, a square [#permalink] New post   17 May 2020, 04:23
Carcass wrote:
Great job :)


Thanks, Carcass :-D
One thing I want to confirm, I received 20+ kudos now. How can I get free tests? and will it be like one test at a time, or I can practice them more than once?
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Re: The figure above shows a solid with thickness of 1, a square [#permalink] New post   17 May 2020, 05:15
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vndnjn wrote:
Carcass wrote:
Great job :)


Thanks, Carcass :-D
One thing I want to confirm, I received 20+ kudos now. How can I get free tests? and will it be like one test at a time, or I can practice them more than once?


When you eligible for the tests you will see the badge under your username.

Give the board time to process it all. You can have full access to all the tests.

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Re: The figure above shows a solid with thickness of 1, a square [#permalink] New post   20 Aug 2022, 01:31
In area of trapeizum, h is the distance between parallel sides. In this question, h= 1.
Why we take h= √2

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The figure above shows a solid with thickness of 1, a square [#permalink] New post   20 Aug 2022, 01:34
vndnjn wrote:
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


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Re: The figure above shows a solid with thickness of 1, a square [#permalink] New post   13 Oct 2023, 17:00
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The figure above shows a solid with thickness of 1, a square [#permalink]
13 Oct 2023, 17:00
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