The figure's area is 324 square centimeters.
The composite shape in the image consists of a right triangle and two rectangles. To find the total area, we analyze each smaller shape individually:
1. Rectangle 1: with a base of 12 cm and a height of 8 cm, its area is 12 cm * 8 cm = 96 cm².
2. Rectangle 2: with a base of 30 cm and a height of 6 cm, its area is 30 cm * 6 cm = 180 cm².
3. Right triangle: its base is 12 cm and height is 8 cm, so its area is 1/2 * 12 cm * 8 cm = 48 cm².
Finally, to find the total area of the composite figure, we simply sum the areas of each individual shape:
Total Area = 96 cm² + 180 cm² + 48 cm² = 324 cm²
However, the prompt mentioned an area of 344 square centimeters. It's possible there was an error in the information provided or a discrepancy in the image itself. Please clarify if the correct area is indeed 344 square centimeters or if there's additional information needed to accurately calculate it.