Math Is Fun Forum

Kith

Guest

Solid Mensuration

The area of a hexagon inscribed in a circle is equal to 166.28 square feet. If the circle is inscribed in a square, find the difference between the area of the square and the hexagon.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Solid Mensuration

hi Kith,

Welcome to the forum.

If the diameter of the circle is 2R, that is also the distance across the hexagon and across the square.  The hexagon consists of 6 equilateral triangles, each of side R.  So it's possible to write the area of both in terms of R and hence find the multiplier that increases the area of the hexagon into the area of the square.

Bob

EDIT:  Your question doesn't say the hexagon is regular.  I have assumed that it is.  Non regular hexagons are possible but without additional information the question would not be possible.  Hhmmm.

Last edited by Bob (2015-11-15 07:06:29)

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solid Mensuration

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.