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# How can i find the area of a polygon if diagonals are 35 and its apothem measures 10cm.

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How can i find the area of a polygon if diagonals are 35 and its apothem measures 10cm.

Jun 21, 2014

#3
+101771
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what is an apothem you ask.

Jun 22, 2014

#1
+3450
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I believe to solve this, we need to know what kind of polygon this is. A polygon simply means "many sides." From the information given, this could be a octagon, a pentagon, a hexagon, we just don't know.

The amount of sides would determine how many diagonals there are and would throw off our area.

Correct me if I'm wrong here...

Jun 21, 2014
#2
+101431
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You are correct, ND.....we could only give a general  formula, but that's all....we would have to know the number of sides.

Jun 21, 2014
#3
+101771
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what is an apothem you ask.

Melody Jun 22, 2014
#4
+28029
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There is no regular polygon with diagonals 35 and apothem 10.  The radius would be 17.5 so the cosine of the angle between an apothem and the nearest radius would be 10/17.5 this means the angle would be

cos-1(10/17.5), so the angle between radii would be 2*cos-1(10/17.5).

$${\mathtt{2}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{10}}}{{\mathtt{17.5}}}}\right)} = {\mathtt{110.300\: \!190\: \!841\: \!908}}$$

360° divided by this doesn't result in an integer!

Jun 22, 2014
#5
+101431
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Thanks for that analysis, Alan.......yep, the info in this problem definitely would need to be "tweaked" to produce a regular figure....

Jun 22, 2014