 Quandaries and Queries What is the total acreage of a pie-shaped piece of land that is: 146' front 85' back 246' each side 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 x = 85 feet y = 146 feet 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 146 = |CD| = |CE| + |EF| + |FD| = |CE| + 85 + |FD| so |FD| = (146 - 85)/2 = 30.5 feet Triangle AFD is a right triangle so, using Pythagoras' Theorem h = |AF| = sqrt(|AD|2 - |FD|2) = sqrt(2462 - 30.52) = 244.1 feet This the area, in square feet is  (146 + 85)/2 244.1 = 28,194.55 There are 23,560 square feet in an acre so the area, in acres is  28,194.55/23,560 = 1.2 Penny Go to Math Central