Math Is Fun Forum

glenn101

Member

Registered: 2008-04-02

Posts: 108

Pyramids

I'm having trouble working out thse 2 questions related to right pyramids with square bases.

1. A right pyramid with a square base is shown in the diagram. The height of the pyramid is 5cm and the square base has sides of length 10cm. The length of a sloping edge in centimetres is.

2. A right pyramid with a square base is shown (sorry can't draw diagram). The square base has sides of length 6cm. The length of each sloping edge is also 6cm. The height of the pyramid in centimetres is.
Could you please explain methods of solving these equations and explain the formula's your using, I havn't done questions related to pyramids in years I've forgotten it all.

Thanks in advance,
Glenn.

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careless25

Real Member

Registered: 2008-07-24

Posts: 560

Re: Pyramids

1. so make it a right angle triangle.

5cm base and 5 cm height.

so square root of 50 is the length of the side in centimeters.

Last edited by careless25 (2008-12-19 13:06:09)

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Pyramids

Thanks for the quick reply careless25 that makes alot more sense now, why didn't I think of that.
Any ideas for the second question?
thanks again.

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Pyramids

It's not quite that simple, because the apex of the pyramid is directly above the centre of the base and so the base length of the triangle isn't just 5cm.

Using Pythagoras to find the base length you get √50, then you can find the sloped height in the same way as before.

For 2, it's a similar thing but backwards. Using the same right-angled triangle as before, this time the base length is √18 and we're told the sloped height (hypotenuse) is 6cm.
You can find the height by using Pythagoras on these.

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glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Pyramids

Hmm I'm following your logic for question 2 mathsy but I get the answer wrong.
The answer according to my sheet is root18.
so do you use the pythagoras theorem for question 2 as follows:

c^2-b^2=a^2
6^2-root18^2=18
root18=3root2
Am I doing something wrong here?

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Pyramids

That looks fine to me.

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Why did the vector cross the road?
It wanted to be normal.

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Pyramids

Thanks mathsy:D
I thought it was right, the teacher said there were errors with this booklet so thanks for that.

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careless25

Real Member

Registered: 2008-07-24

Posts: 560

Re: Pyramids

sry i was watching a movie so i couldnt reply.
BUt anyways mathsy solved it for you.

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Pyramids

Don't mention it careless, its good to know people care about helping others

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