The area of the pentagon is that of a rectangle of length <i>b</i> and 
breadth <i>a</i> plus that of a triangle of base <i>b</i> and height (<i>c</i> <font face="symbol">-</font
> <i>a</i>), 
i.e.





<br clear="all" /><table border="0" width="100%"><tr><td>
<table align="center"><tr><td nowrap="nowrap" align="center">
<i>ab</i> + </td><td nowrap="nowrap" align="center">
1<hr noshade="noshade" size="1" />2<br /></td><td nowrap="nowrap" align="center">
(<i>c</i> <font face="symbol">-</font
> <i>a</i>) = </td><td nowrap="nowrap" align="center">
1<hr noshade="noshade" size="1" />2<br /></td><td nowrap="nowrap" align="center">
<i>b</i>(2<i>a</i> + <i>c</i> <font face="symbol">-</font
> <i>a</i>) = </td><td nowrap="nowrap" align="center">
1<hr noshade="noshade" size="1" />2<br /></td><td nowrap="nowrap" align="center">
<i>b</i>(<i>a</i> + <i>c</i>)</td></tr></table>
</td></tr></table>




[The area may also be considered to be the sum of the areas of two trapezia 
which have parallel sides <i>a</i> and <i>c</i> and whose heights have total length 
<i>b</i>.]  




    


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