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23 Jun 2020, 06:41
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E
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Difficulty:
75%
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Question Stats:
41% (02:11) correct
59%
(01:45)
wrong
based on 39
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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?
A. 38
B. 50
C. \(34 \sqrt{2}\)
D. \(34+4 \sqrt{2}\)
E. \(34+16 \sqrt{2}\)
Attachment:
1.jpg [ 16.88 KiB | Viewed 1420 times ]
yashikaaggarwal
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23 Jun 2020, 07:24
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Area of solid = 4*Area of trapezoid + Area of square 3 + Area of square 5
Area of trapezoid = average of bases*slant height of solid(other than 4 corners)
Slant height^2 = width^2+1^2 (since the difference between two squares = 2, equally distributed among both sides. So 1 unit in excess on each side.)
=> Slant height = √1^2+1^2
=> (3+5/2)*√1^2+1^2
=> 4√2
Area of four trapezoid = 4*4√2 = 16√2
Area of Square = 5^2 = 25
Area of square = 3^2 = 9
Total area = 16√2+9+25 => 16√2+34
IMO E
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Area of trapezoid = average of bases*slant height of solid(other than 4 corners)
Slant height^2 = width^2+1^2 (since the difference between two squares = 2, equally distributed among both sides. So 1 unit in excess on each side.)
=> Slant height = √1^2+1^2
=> (3+5/2)*√1^2+1^2
=> 4√2
Area of four trapezoid = 4*4√2 = 16√2
Area of Square = 5^2 = 25
Area of square = 3^2 = 9
Total area = 16√2+9+25 => 16√2+34
IMO E
Posted from my mobile device
23 Jun 2020, 22:15
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Total surface area = Area of 4 trapezoids + Area of top square + Area of bottom square
=> TSA = \(4*0.5*(3+5)*\sqrt{height^2+(width on each side)^2} + 3^2 + 5^2\)
=> TSA = \(4*0.5*(3+5)*\sqrt{1^2+1^2} + 3^2 + 5^2\)
=> TSA = \(16\sqrt{2} + 34\)
Ans: E
=> TSA = \(4*0.5*(3+5)*\sqrt{height^2+(width on each side)^2} + 3^2 + 5^2\)
=> TSA = \(4*0.5*(3+5)*\sqrt{1^2+1^2} + 3^2 + 5^2\)
=> TSA = \(16\sqrt{2} + 34\)
Ans: E
