1. **State the problem:** We need to find the area of an L-shaped composite figure with outer dimensions 14 inches by 14 inches and an inner cutout of 7 inches by 7 inches. 2. **Formula and approach:** The area of the composite figure can be found by subtracting the area of the inner cutout from the area of the large outer square. 3. **Calculate the area of the outer square:** $$\text{Area}_{outer} = 14 \times 14 = 196 \text{ square inches}$$ 4. **Calculate the area of the inner cutout square:** $$\text{Area}_{cutout} = 7 \times 7 = 49 \text{ square inches}$$ 5. **Calculate the area of the L-shaped figure:** $$\text{Area}_{L} = \text{Area}_{outer} - \text{Area}_{cutout} = 196 - 49 = 147 \text{ square inches}$$ 6. **Final answer:** The area of the L-shaped composite figure is **147 square inches**.