Starting at home plate, all the way around in a square, each base is 90 feet apart. Then the pitcher's rubber is 60 feet 6 inches away from home plate.
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no
yes it does
The distance across the diamond is 114.6 feet.
8100 ft2
Yes, the common name for an equiangular equilateral quadrilateral would be a square, a special instance of a rhombus (four sided figure with equal sides) which is a common interpretation of "diamond" in two dimensions. If by diamond you mean "kite" then no, by definition kites are not equiangular.