Step-by-step explanation:
A = (1, 3)
B = (3, 6)
C = (9, 2)
D = (7, -1)
the distance between 2 points is given by the Pythagoras equation based on the coordinate differences as legs of virtual right-angled triangles.
AD for example we get from
AD² = (7-1)² + (-1 - 3)² = 6² + (-4)² = 36 + 16 = 52
AD = sqrt(52) = sqrt(4×13) = 2×sqrt(13)
and AB we get from
AB² = (3-1)² + (6-3)² = 2² + 3² = 4 + 9 = 13
AB = sqrt(13)
the perimeter of the given rectangle is
2×sqrt(52) + 2×sqrt(13) = 2×2×sqrt(13) + 2×sqrt(13) =
= 6×sqrt(13) = 21.63330765...
and the area of the rectangle is
2×sqrt(13)×sqrt(13) = 2×13 = 26
