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# A pyramid has a square base of 6 cm, and the four lateral faces are fo

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Math Expert
Joined: 02 Sep 2009
Posts: 50016
A pyramid has a square base of 6 cm, and the four lateral faces are fo  [#permalink]

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25 Feb 2015, 03:00
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Question Stats:

85% (01:37) correct 15% (02:00) wrong based on 105 sessions

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A pyramid has a square base of 6 cm, and the four lateral faces are four congruent equilateral triangles. What is the total surface area of the pyramid in square cm?

(A) $$36 + 18*\sqrt{3}$$

(B) $$36 + 36*\sqrt{3}$$

(C) 72

(D) $$72 + 36*\sqrt{3}$$

(E) $$72 + 72*\sqrt{3}$$

Kudos for a correct solution.

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Re: A pyramid has a square base of 6 cm, and the four lateral faces are fo  [#permalink]

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25 Feb 2015, 07:35
1
Congruent equilateral triangles means all the triangles are equal. let it be x. Area of equilateral triangle = $$\frac{x^2 *sqrt(3)}{4}$$= $$\frac{36*sqrt(3)}{4}$$
we have 4 triangles and base so total surface area= 36 + 36*sqrt(3) answer B
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Posts: 50016
Re: A pyramid has a square base of 6 cm, and the four lateral faces are fo  [#permalink]

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02 Mar 2015, 05:22
Bunuel wrote:
A pyramid has a square base of 6 cm, and the four lateral faces are four congruent equilateral triangles. What is the total surface area of the pyramid in square cm?

(A) 36 + 18*sqrt(3)
(B) 36 + 36*sqrt(3)
(C) 72
(D) 72 + 36*sqrt(3)
(E) 72 + 72*sqrt(3)

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

First of all, of course, the base has an area of 36. For the lateral surfaces, it would be helpful to remember the formula for the area of an equilateral triangle. If that’s unfamiliar, take a look at this post: http://magoosh.com/gmat/2012/gmat-math- ... emorizing/

The area of one equilateral triangle is $$A = \frac{(s^2*\sqrt{3})}{4}$$. We know the side of the equilateral triangle must be the same as the square: s = 6. Thus, one of these equilateral triangles has an area of $$A = \frac{(6^2*\sqrt{3})}{4} = 9*\sqrt{3}$$. There are four identical triangles, so their combined area is $$A = 36*\sqrt{3}$$. Now, add the square base, for a total surface area of $$A = 36 + 36*\sqrt{3}$$.

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Joined: 02 Sep 2009
Posts: 50016
Re: A pyramid has a square base of 6 cm, and the four lateral faces are fo  [#permalink]

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02 Mar 2015, 05:30
Bunuel wrote:
A pyramid has a square base of 6 cm, and the four lateral faces are four congruent equilateral triangles. What is the total surface area of the pyramid in square cm?

(A) 36 + 18*sqrt(3)
(B) 36 + 36*sqrt(3)
(C) 72
(D) 72 + 36*sqrt(3)
(E) 72 + 72*sqrt(3)

Kudos for a correct solution.

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Re: A pyramid has a square base of 6 cm, and the four lateral faces are fo  [#permalink]

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21 Sep 2018, 08:16
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Re: A pyramid has a square base of 6 cm, and the four lateral faces are fo &nbs [#permalink] 21 Sep 2018, 08:16
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