Kite (a quadrilateral with two pairs of adjacent equal sides) has coordinates and What is the area of given that the area of a kite is equal to half the product of its diagonals?
You can use the distance formula to find the lengths of the diagonals:
Distance = sqrt[ (x2 - x1)2 + (y2 - y1)2 ]
To find the distance AC: Distance = sqrt[ (12 - 0)2+ (-2 - 12)2 ]
To find the distance BD: Distance = sqrt[ (7 - 1)2 + (8 - 0)2 ]
Then use the area of a kite (that you gave with your question).
Can you take it from here?