1. **State the problem:** Find the area of an irregular polygon composed of three rectangular segments with right angles. 2. **Analyze the figure:** The base length is 13 inches, height on left and right sides is 6 inches each. There are two rectangular cutouts on the top side, each 4 inches wide and 2 inches deep, separated by a 5-inch horizontal segment. 3. **Formula:** Area of polygon = Area of large rectangle - Areas of cutouts. 4. **Calculate the area of the large rectangle:** $$\text{Area}_{\text{large}} = 13 \times 6 = 78$$ square inches. 5. **Calculate the area of each cutout:** Each cutout is $4$ inches wide and $2$ inches deep. $$\text{Area}_{\text{cutout}} = 4 \times 2 = 8$$ square inches. 6. **Calculate total cutout area:** There are two cutouts. $$\text{Area}_{\text{cutouts}} = 2 \times 8 = 16$$ square inches. 7. **Calculate the area of the figure:** $$\text{Area} = 78 - 16 = 62$$ square inches. **Final answer:** The area of the figure is $62$ square inches.