<PRE><B>Question 739070</B>
Additional info is needed for a numeric answer.  Without knowing x or y or some other relation between them, the answer will contain at least one variable.&lt;P&gt;
A = 1/2 a *P where a is apothem and P is perimeter.&lt;P&gt;
1/2 * 1/2 y * 10x = 5xy/2:  Answer 1.&lt;P&gt;
You can go further by cutting the pentagon into 5 triangles, and cutting each of those into two right triangles with height 1/2 y and base x.  The triangles thus formed are 36 (opposite the side length x), 54 (opposite the side length 1/2 y) 90 triangles.  &lt;P&gt;
Then tan(36) = x/(1/2y) so x = 1/2 y * tan(36)&lt;P&gt;
Substitute that back into the 5xy/2 gives 5*(1/2 y *tan(36))*y /2 = {{{5*y^2*tan(36)/4}}}  Answer 2.&lt;P&gt;
tan(54) = y/2x and 2x*tan(54) = y&lt;P&gt;
Then 5xy/2 = 5x*2x*tan(54)/2 = {{{5x^2*tan(54)}}}  Answer 3.&lt;P&gt;
Those three answers are equivalent.
&lt;P&gt;Hope the solution helped.  Sometimes you need more than a solution.  Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)
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