Answer:
4 cm^2
Explanation:
A = hb/2
h is BD and b is AC
Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
Pythagorean theorem: c^2 = a^2 + b^2
AB^2 = BD^2 + AD^2
=> BD^2 = AB^2 - AD^2 = (2√5)^2 - (3√2)^2 = 20 - 18 = 2
=> BD = √2
AC = AD + DC = 3√2 + √2 = 4√2
Area: A = BD*AC*1/2 = √2 * 4√2 * 1/2 = 8/2 = 4 cm^2