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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

Let ABCDE be a pyramid, where the base ABCD is a square of side length 10. The total surface area of pyramid ABCDE (including all five faces) is 260. Let M, N, P, and Q be the midpoints of \overline{AE}, \overline{BE}, \overline{CE}, and \overline{DE}, respectively. Find the total surface area of frustum ABCDMNPQ.

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,501

hi mathstudent2000

Welcome to the forum.

The smaller pyramid MNPQE is an exact copy of the larger, just scaled down by a scale factor x 0.5

So its surface area will be scaled down by the length scale factor squared (x 0.25)

So you can calculate its surface area.

Now, if we just wanted the sloping surface area, it would be easy enough to get this by subtraction.

But there's an added complication: you are asking for the area including the top square face of the frustrum.

But you know the length of a side of the base, so you can get the size of the smaller square base, and hence finish off the question.

Hopefully, that's enough of a hint; post back if you need more help or with an answer for checking.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

thanks

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,501

You're welcome.

So did you get it right? / or if not yet submitted, do you want to post your answer?

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**SPARKS_CHAN****Member**- Registered: 2014-12-05
- Posts: 15

bob bundy wrote:

You're welcome.

So did you get it right? / or if not yet submitted, do you want to post your answer?

Bob

I'm working on the same problem.

Is the answer not 220?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,501

hi SPARKS_CHAN

Have you forgotten the area of the top of the frustrum ?

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**numbergeek****Member**- Registered: 2016-02-08
- Posts: 4

I am also working on this problem and I don't understand why 220 is not correct. The total surface area of the pyramid is 260. The scale factor is .25 (.5 squared). I have 260 - 260(.25) + surface area of the smaller square. Length of the larger square is 10, so smaller square side length is 5. So I think the correct calculation is 260 - 65 + 25 which is 220. but that answer is wrong.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,501

hi numbergeek

Welcome to the forum.

The total surface area of the pyramid is 260. The scale factor is .25 (.5 squared). I have 260 - 260(.25) + surface area of the smaller square. Length of the larger square is 10, so smaller square side length is 5. So I think the correct calculation is 260 - 65 + 25 which is 220.

Thanks for including your working. That makes it much easier for me to see what is going wrong.

The scale factor principle applies to similar shapes. So you can use it for the four large sloping sides and the equivalent smaller sloping sides. For the large, the total area of all four is 260 - 10x10 = 160. So the area of the smaller sloping sides is 160 x 0.25 = 40. So for the frustum the area of the sloping sides is 160 - 40 = 120. Now add in the top and bottom and you're finished.

Note: Each large sloping side is a triangle ... area = 160/4 = 40. So each equivalent triangle in the small is 40 x 0.25 = 10, so all four is 10x4 = 40. So you can see that the scale factor principle works for each triangle or all four together.

You cannot do 260 - 260 x 0.25 because it doesn't take account of the bottom square properly. It isn't scaled down. Stick to working out the sloping area first and you should be OK.

Hope that helps,

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**evene****Member**- Registered: 2015-10-18
- Posts: 141

Do not look below if you do not want to see the answer! Cheat at your own risk!

I am getting an answer of not 220, but a surface area of 245.

Also, how do you do the [Hint] tab that leads you to a new page with the answer? Bobbym does this all the time.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,289

Hi evene;

You use the 'hide' tags.

In the following two examples I've included a space before "hide" in the opening tag. You must remove that space in each example for them to work for you, but their inclusion enabled me to prevent my text from turning into hide boxes.

This:

[ hide=Hint]Type your text here...[/hide]

will give you this:

And this:

[ hide]Type your text here...[/hide]

will give you this:

Click on the two boxes to display their contents.

If you click on the "Quote" button in the bottom right-hand corner of my post you'll see exactly how I did it for my two boxes.

You can also just copy my examples into your post and experiment there.

*Last edited by phrontister (2016-02-08 14:49:34)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,501

hi evene,

That's the answer I'm getting too.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**numbergeek****Member**- Registered: 2016-02-08
- Posts: 4

bob bundy wrote:

hi numbergeek

Welcome to the forum.

You cannot do 260 - 260 x 0.25 because it doesn't take account of the bottom square properly. It isn't scaled down. Stick to working out the sloping area first and you should be OK.

Hope that helps,

Bob

Thanks, Bob. That helped me a lot. I hadn't thought about it that way and couldn't figure out what I was doing wrong.

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**evene****Member**- Registered: 2015-10-18
- Posts: 141

Thanks Phrontister!

*Last edited by evene (2016-02-09 13:49:00)*

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