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To find the area of the quadrilateral, we need to split it into two triangles and then find the area of each triangle.
First, find the area of triangle ABC:
Area = 1/2 * base * height
Area of triangle ABC = 1/2 * 6 cm * 4 cm = 12 cm^2
Next, find the area of triangle ACD:
Area = 1/2 * base * height
Area of triangle ACD = 1/2 * 4 cm * 3 cm = 6 cm^2
Now, add the areas of the two triangles to find the total area of the quadrilateral:
Total area = 12 cm^2 + 6 cm^2
Total area = 18 cm^2
Therefore, the area of the quadrilateral is 18 cm^2.