Question 936391
<pre>
We use Bretschneider's formula:

If a, b, c, and d are the sides of a convex quadrilateral, and s is the
semiperimeter, {{{s=(a+b+c+d)/2}}} and {{{alpha}}} and {{{gamma}}} are two opposite angles, 
then the area A of the quadrilateral is given by

{{{A=sqrt((s-a)(s-b)(s-c)(s-d)-abcd(1^""+cos(alpha+gamma)))}}}

First we calculate s with a=10, b=5, c=14.14, d=15,

{{{s=semiperimeter=(a+b+c+d)/2=(10+5+14.14+15)/2=44.14/2=22.07}}}

Then using that and {{{alpha+gamma="225°"}}},

{{{A=sqrt((22.07-10)(22.07-5)(22.07-14.14)(22.07-15)-(10)(5)(14.14)(15)(1^""+cos("225°")))}}}


A = 91.89795801035699017470925314054801987941948129813875441889863... cm².

Edwin</pre>