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#1 2015-06-23 11:46:12

Argh
Guest

Area of a Rhombus

I was asked a question today and I cant figure it out. A square with side A has two equilateral triangles inscribed within it also with side A. The triangles cross to form a rhombus. What is the area of the Rhombus in terms of A?

#2 2015-06-23 12:17:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Area of a Rhombus

Hi;


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.

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#3 2015-06-23 20:07:17

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Area of a Rhombus

hi Argh

Welcome to the forum.

I cannot make a diagram with this information.  I made a square and called one side A . Then I made one equilateral triangle inside the square with one side A.  I cannot make another.  Did you mean that the second triangle has side B where B is opposite to A ?

EDIT:  Ah ha!  Just read the second post.  Ok here we go:

GI8aln2.gif

#Using trig. you can work out EJ and GI and as you know IJ you can work out EG.

Angle HGE = 30 so you can work out HF. 

The rhombus is 4 right angled triangles so its area is half EG x HF.

Bob

Last edited by Bob (2015-06-23 20:24:14)


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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#4 2015-06-24 20:56:16

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,810

Re: Area of a Rhombus

Hi;

Deducting the area of the square from the sum of the areas of the four triangles that together fill the square gives the area of the only overlapped region: the rhombus.

The pair of isosceles triangles is congruent (as is the pair of equilateral triangles), and, using the area formulas for these triangles, I got the following in terms of A:

HtV9PVh.png

Last edited by phrontister (2017-02-27 00:34:43)


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