The area of the pentagon is that of a rectangle of length b and breadth a plus that of a triangle of base b and height (c-a), i.e.

ab+

1 2

b(c-a)=

1 2

b(2a+c-a)=

1 2

b(a+c)

.

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