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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: 7,271

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: 7,271

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: 7,271

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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