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

Guest Jun 21, 2014

#1**+5 **

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...

NinjaDevo
Jun 21, 2014

#2**+3 **

You are correct, ND.....we could only give a general formula, but that's all....we would have to know the number of sides.

CPhill
Jun 21, 2014

#4**+5 **

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).

$${\mathtt{2}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{10}}}{{\mathtt{17.5}}}}\right)} = {\mathtt{110.300\: \!190\: \!841\: \!908}}$$

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

Alan
Jun 22, 2014