ABD is a triangle, C lies on BD. AD=BD=√2/2 and CD=√3/3. Find the EXACT area of ABC. (all measurements are in cm)

Formula/ Facts you may need for this question: !!! area of a triangle = base * height * 0.5 !!! multiplying fractions = nominators multiplied over denominators multiplied
Step 1: whole triangle area ABD = √2/2√2/21/2 = (√2√21)/(222) = √(22)/8 = √4/8 = 2/8 =1/4
Step 2: ABD- (area wanted) ABC = ACD area = √2/2√3/31/2 = (√2√31)/(232) = √(23)/12 = √6/12
Step 3: (area wanted) ABC = ABD - ACD = 1/4 - √6/12