Consider △ ABD
Using Pythagoras theorem
AB2 = AD2 + BD2
By substituting the values
AB2 = 122 + 162
On further calculation
AB2 = 144 + 256
By addition
AB2 = 400
By taking out the square root
AB = √400
So we get
AB = 20cm
We know that the area of △ ABD = ½ × b × h
It can be written as
Area of △ ABD = ½ × AD × BD
By substituting the values
Area of △ ABD = ½ × 12 × 16
On further calculation
Area of △ ABD = 96 cm2
Consider △ ABC
So the area of the shaded region = Area of △ ABC – Area of △ ABD
By substituting the values
Area of the shaded region = 480 – 96 = 384 cm2
Therefore, the area of the shaded region is 384 cm2.
