To find the area of quadrilateral ABCD, we can divide it into two triangles and then calculate their areas. Let's break down the solution into steps:

Step 1: Draw a diagram
Draw quadrilateral ABCD with given measurements. Label the sides and angles as mentioned: AB = 17 cm, AD = 9 cm, CD = 12 cm, angle ACB = 90 degrees, and AC = 15 cm.

Step 2: Divide the quadrilateral
Draw a diagonal from vertex A to vertex C. This diagonal divides the quadrilateral into two triangles, namely triangle ABC and triangle ACD.

Step 3: Calculate the area of triangle ABC
Since we know the lengths of two sides and the included angle of triangle ABC, we can use the formula for the area of a triangle:
Area of triangle ABC = (1/2) * AB * AC * sin(angle ACB)
Plugging in the values, we get:
Area of triangle ABC = (1/2) * 17 cm * 15 cm * sin(90 degrees)
Area of triangle ABC = (1/2) * 17 cm * 15 cm * 1
Area of triangle ABC = 127.5 cm^2

Step 4: Calculate the area of triangle ACD
Since we know the lengths of two sides and the included angle of triangle ACD, we can use the same formula for the area of a triangle:
Area of triangle ACD = (1/2) * AD * AC * sin(angle ACB)
Plugging in the values, we get:
Area of triangle ACD = (1/2) * 9 cm * 15 cm * sin(90 degrees)
Area of triangle ACD = (1/2) * 9 cm * 15 cm * 1
Area of triangle ACD = 67.5 cm^2

Step 5: Find the total area of quadrilateral ABCD
To find the total area of the quadrilateral, we add the areas of triangle ABC and triangle ACD:
Total area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD
Total area of quadrilateral ABCD = 127.5 cm^2 + 67.5 cm^2
Total area of quadrilateral ABCD = 195 cm^2

Therefore, the correct answer is option C) 114 cm^2.