Don't Get This One Wrong on the Test - It's Actually EASY

Can you get this one right? Find the area of the yellow half circle inside a 6 cm by 8 cm right triangle, with no radius given. The trick is a smaller copy of the big triangle hiding at the top. CHAPTERS 0:00 The puzzle 0:32 Drawing it again 1:03 The area of a half circle 1:23 Two radii and a square 2:09 The corners 2:32 Two smaller copies 3:16 One proportion 3:41 Solving for r 4:35 Checking r on the squares 4:51 The yellow area 5:25 Back to the picture