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The figure shown represents a solid pyramid with a square base of leng

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The figure shown represents a solid pyramid with a square base of leng  [#permalink]

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New post 30 May 2018, 09:12
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Difficulty:

  65% (hard)

Question Stats:

50% (02:47) correct 50% (02:02) wrong based on 37 sessions

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Attachment:
Geometry_Prblm.PNG
Geometry_Prblm.PNG [ 24.07 KiB | Viewed 503 times ]


The figure shown represents a solid pyramid with a square base of length 10. If EO is an
imaginary line segment representing the height of the pyramid and EO = 12, what is the
area of the four sides(excluding the base) of the pyramid?

A. 480
B. 260
C. 240
D. 130
E. 120

Source: Experts Global

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The figure shown represents a solid pyramid with a square base of leng  [#permalink]

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New post 30 May 2018, 09:29
pushpitkc wrote:
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The figure shown represents a solid pyramid with a square base of length 10. If EO is an
imaginary line segment representing the height of the pyramid and EO = 12, what is the
area of the four sides(excluding the base) of the pyramid?

A. 480
B. 260
C. 240
D. 130
E. 120

Source: Experts Global


Attachment:
pyramid_1.jpg
pyramid_1.jpg [ 26.29 KiB | Viewed 473 times ]


Each side of the pyramid will be a triangle with one side of the square as its base. To find the area of the side we only need to know the HEIGHT of the triangle.

Now if you drop a perpendicular line from point O to any of the sides of the base, lets say on side CD, then let's assume the point meets the side CD at point P.

Now we have a right triangle EOP, with \(EO=12\), \(OP=\frac{10}{2}=5\) and we need the hypotenuse \(PE\) (which will be the height of the triangular side of the pyramid)

So \(PE=13\) (12-5-13 triplet)

Hence Area of 4 triangular sides of pyramid \(= \frac{1}{2}*10*13*4=260\)

Option B
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Re: The figure shown represents a solid pyramid with a square base of leng  [#permalink]

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New post 09 Jun 2018, 20:26
Area of a Pyramid can be found out using the formulae : 2a sq.rt(a^2/4 + h^2) where a is the length of the base of the pyramid and h is the height

So,

2*10 sq.rt (100/4 + 144)
= 20 sq. rt (169)
=20 * 13
=260
GMAT Club Bot
Re: The figure shown represents a solid pyramid with a square base of leng &nbs [#permalink] 09 Jun 2018, 20:26
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The figure shown represents a solid pyramid with a square base of leng

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