The Mango Orchard Division

The Story: In a small village near Ratnagiri, old Ramabai has four grown children — Sunita, Mohan, Priya, and Dev — and she has decided it is time to divide her mango orchard among them before she gets any older. The orchard is a perfect square plot, 100 metres on each side. Ramabai has one condition that she will not bend on: each child must receive a plot of exactly equal area. She also wants each child's plot to be a single connected piece of land — no child should end up with two separate patches. Sunita, who studied geometry in college, starts sketching possible divisions in her notebook. Mohan says it is impossible to divide a square into four equal connected pieces that are not simply four smaller squares. Priya laughs and says she can think of at least five different ways to do it. Dev pulls out a piece of paper and asks: 'How many geometrically distinct ways can we divide a 4x4 grid into four congruent connected pieces?' The Challenge: How many distinct ways can you divide a 4x4 grid into exactly four congruent (same shape and size) connected pieces, each containing exactly 4 cells?