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505-555 (Easy)|   Geometry|      
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A pyramid has a square base of 6 cm, and the four lateral faces are fo 25 Feb 2015, 03:00
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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) \(72 + 72*\sqrt{3}\)


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A pyramid has a square base of 6 cm, and the four lateral faces are fo 02 Mar 2015, 05:22
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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)


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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: https://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 \(A = 36 + 36*\sqrt{3}\).

Answer = B.
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A pyramid has a square base of 6 cm, and the four lateral faces are fo 25 Feb 2015, 07:35
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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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A pyramid has a square base of 6 cm, and the four lateral faces are fo 02 Mar 2015, 05:30
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Bunuel
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)


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Check other 3-D Geometry Questions in our Special Questions Directory.
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A pyramid has a square base of 6 cm, and the four lateral faces are fo 16 Feb 2020, 22:57
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Bunuel
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: https://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 \(A = 36 + 36*\sqrt{3}\).

Answer = B.
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is it the total surface area formula?

Surface Area = Area of equilateral triangle + square base?
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A pyramid has a square base of 6 cm, and the four lateral faces are fo 17 Feb 2020, 00:04
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Bunuel
Bunuel
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: https://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 \(A = 36 + 36*\sqrt{3}\).

Answer = B.

is it the total surface area formula?

Surface Area = Area of equilateral triangle + square base?
Show more

The surface area of a pyramid is the sum of the areas of its faces.

In the question above, the pyramid has a square base and the four lateral faces of four congruent equilateral triangles. So, the total surface area of that pyramid is (area of the base) + 4*(area of the equilateral triangle).
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A pyramid has a square base of 6 cm, and the four lateral faces are fo 07 Oct 2023, 03:18
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