Final answer:
To find the area of quadrilateral ABCD, split it into two triangles, calculate the lengths of the sides using the Pythagorean theorem, and use the area formula for triangles.
Step-by-step explanation:
To find the area of quadrilateral ABCD, we can split it into two triangles: triangle ABC and triangle ACD. First, we can find the length of AB by using the Pythagorean theorem: AB = sqrt(AD^2 - BD^2) = sqrt(12^2 - 10^2) = sqrt(144 - 100) = sqrt(44) = 2sqrt(11).
Then, we can find the length of AC using the Pythagorean theorem: AC = sqrt(AD^2 + DC^2) = sqrt(12^2 + 10^2) = sqrt(144 + 100) = sqrt(244) = 2sqrt(61).
Next, we can find the area of each triangle by using the formula: area = (1/2) * base * height. For triangle ABC, the base is AB and the height is BC. For triangle ACD, the base is AC and the height is DC.
Finally, we can calculate the total area of the quadrilateral by adding the areas of the two triangles together.