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Problem: Dividing a Cake
For Acute Alice's birthday, Obtuse Ollie bought a square cake, 9 inches on each side. They wanted to cut into three equal pieces.
Ollie was going to cut the cake as shown at the left below, but Alice said she wouldn't want the piece in the middle.
Alice did some figuring and cut the cake as shown at the right above. Find the area of the six triangles formed.
Area triangle AMB = area triangle AMD = 20.25 in^2.
Area triangle BMX = area triangle DMY = 6.95 in^2.
Area triangle CMX = area triangle CMY = 13.5 in^2.