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

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
The figure shown represents a solid pyramid with a square base of leng  [#permalink]

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30 May 2018, 09:12
2
00:00

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 [ 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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Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
The figure shown represents a solid pyramid with a square base of leng  [#permalink]

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30 May 2018, 09:29
pushpitkc wrote:
Attachment:
The attachment Geometry_Prblm.PNG is no longer available

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 [ 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
Intern
Joined: 04 May 2018
Posts: 24
GMAT 1: 650 Q46 V34
Re: The figure shown represents a solid pyramid with a square base of leng  [#permalink]

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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
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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