Calculate the length of AB
c = √(36+9) = 3√5
Calculate the length of BC
a = √(36+9) = 3√5
Calculate the length of AC.
b = √(0+36) = 6
Calculate the perimeter of ΔABC
p = 6√5 + 6
Half the perimeter is
s = 3 + 3√5
s-a = 3
s-b = 3√5 - 3
s-c = 3
Note that
(3√5 + 3)(3√5 - 3) = 45 - 9 = 36.
Calculate the area of ΔABC.
A = √[(3√5 + 3)(3)(3√5 - 3)(3)]
= 3(6)
= 18
The area of the rhombus is twice the area of ΔABC, so it is 36 units².
Answer: 36