Quandaries
and Queries 

What is the total acreage
of a pieshaped piece of land that is: The front and back lines are fairly straight....a trapezoidal shape. Thanks, Doak 

Hi Doak, The area of a trapezoid is the average of the lengths of the parallel sides, times the distance between these two sides.
area = ^{(x + y)}/_{2} h A development of this expression can be found in the answer to a previous problem. You sent us the lengths of the two parallel sides
Since the lengths of the other two sides are equal, the symmetry in the diagram below can be used to show that triangles AFD and BCD are congruent.
Thus CE = FD and thus
so
Triangle AFD is a right triangle so, using Pythagoras' Theorem
This the area, in square feet is
There are 23,560 square feet in an acre so the area, in acres is
Penny 

