Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A pyramid with four equal-sized flat surfaces and a base of [#permalink]

Show Tags

16 Feb 2013, 13:30

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

72% (03:11) correct
28% (01:59) wrong based on 104 sessions

HideShow timer Statistics

A pyramid with four equal-sized flat surfaces and a base of 36 ft2 has a height of 10 feet. What is the total surface area of the pyramid, excluding the base?

the book's answer description sort of says it's a right triangle without really explaining how we know that..can anyone help out with understanding that as well?

If it is a pyramid with four equal faces then the bases of all the faces are equal and therefore the base of the pyramid is a square. Because the base is a square it has four 90 degree angles. Because the triangles are equal, each one the the squares right angles is being cut in half (bisected) so that the triangles are each 45-45-90 or right isosceles. You can also look at it this way: the four angles at the top the pyramid added together mus equal 360 degrees. The 4 triangles are equal therefore the angles are equal and 360/4 is 90.

Let me know if you need more advice on this. Happy studies!

HG.
_________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

Re: A pyramid with four equal-sized flat surfaces and a base of [#permalink]

Show Tags

16 Feb 2013, 16:07

HerrGrau wrote:

Hi there,

If it is a pyramid with four equal faces then the bases of all the faces are equal and therefore the base of the pyramid is a square. Because the base is a square it has four 90 degree angles. Because the triangles are equal, each one the the squares right angles is being cut in half (bisected) so that the triangles are each 45-45-90 or right isosceles. You can also look at it this way: the four angles at the top the pyramid added together mus equal 360 degrees. The 4 triangles are equal therefore the angles are equal and 360/4 is 90.

Let me know if you need more advice on this. Happy studies!

HG.

Thanks as always. Could you also show the steps to solve for the answer?? Geometry really isn't my thing. :/

You are very welcome! I looked at this too quickly though. Ignore the above, see below.

So the base is 36. Therefore the area of the square is 36. So if we call each side of the square "S" then S*S = 36 and S = 6. Now we need to find the area of one of the triangles and then multiply that area by 4 and we will have the surface area of the pyramid (without counting the base). So drop the height from the the top of the pyramid straight down to the base and draw a line there connecting to the side of the square (this will be right at the midpoint of the side of the square). That is a right triangle and you can use Pythagorean theorem to find the third side which is the height of our triangle faces. So 10^2 + 3^2 = C^2 109 = C^2 C=109^1/2.

Now find the area: BH/2 6*109^1/2/2 = 3*109^1/2. And multiply that area by 4 because there are four equal triangular faces. 12*109^1/2

Let me know if you have any questions. I know that it can be difficult to visualize without a diagram.

HG.
_________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

Re: A pyramid with four equal-sized flat surfaces and a base of [#permalink]

Show Tags

18 May 2013, 19:49

HerrGrau wrote:

You are very welcome! I looked at this too quickly though. Ignore the above, see below.

So the base is 36. Therefore the area of the square is 36. So if we call each side of the square "S" then S*S = 36 and S = 6. Now we need to find the area of one of the triangles and then multiply that area by 4 and we will have the surface area of the pyramid (without counting the base). So drop the height from the the top of the pyramid straight down to the base and draw a line there connecting to the side of the square (this will be right at the midpoint of the side of the square). That is a right triangle and you can use Pythagorean theorem to find the third side which is the height of our triangle faces. So 10^2 + 3^2 = C^2 109 = C^2 C=109^1/2.

Now find the area: BH/2 6*109^1/2/2 = 3*109^1/2. And multiply that area by 4 because there are four equal triangular faces. 12*109^1/2

Let me know if you have any questions. I know that it can be difficult to visualize without a diagram.

HG.

Okay let's see if I understand this. The reason for applying the Pythagorean Theorem is because the sides are at an angle. Thus the 10 ft. height of the pyramid is not the height of the sides?
_________________

Re: A pyramid with four equal-sized flat surfaces and a base of [#permalink]

Show Tags

23 Jun 2013, 15:38

2

This post received KUDOS

So this is what I get from this question.

1 Square with 36 sq feet or 6' x 6' (doesn't count because question stem excludes it) 4 Right Triangles with a height of 10 when they are connected by all sides and base.

The question tries to trick you because when the 4 triangles are tilted and connected the height is 10, but the real height is the hypotenuse. Think about when you see a pyramid from the side view.

The height from the apex (top of the pyramid) straight down would be 10. We're trying to find the hypotenuse. So use the pyth theorem. a^2 + b^2 = c^2 or 10^2 + 3^2 (half of the base because we're looking for hyp not area)=sq 109

Now we have real height of the triangle. This is the real height of the face of the triangle because it's laid down on a slant (I'm repetitive but it's important)

From here we can just do find the area. 1/2(b)(h)= .5(6)(sq109) = 3 sq(109) Since there are 4 triangles, 4 x 3 sq(109) = 12 sq (109)

Re: A pyramid with four equal-sized flat surfaces and a base of [#permalink]

Show Tags

23 Jun 2013, 20:07

4

This post received KUDOS

1

This post was BOOKMARKED

From Figure, Apex to base be height 'h' =10 we know base b*b =36 => b=6

S = (h^2+ (b/2)^2)^1/2 = (10^2+3^2)^1/2 =109 ^0.5 SO area of the flat surface with height(S) = 109^0.5 * 3 Area of four flat surfaces = 4*3*109^0.5 =12*109^0.5

Re: A pyramid with four equal-sized flat surfaces and a base of [#permalink]

Show Tags

14 Nov 2016, 01:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...