1. **Problem 1: Find the area of the irregular polygon (in inches).** The figure is composed of a rectangle and a right triangle on top. 2. **Formula and rules:** - Area of rectangle = length \times width - Area of right triangle = \frac{1}{2} \times base \times height 3. **Calculate the area of the rectangle:** - Given dimensions: length = 30 inches, width = 25 inches - Area_rectangle = 30 \times 25 = 750 \text{ square inches} 4. **Calculate the area of the right triangle:** - Given dimensions: base = 15 inches, height = 8 inches - Area_triangle = \frac{1}{2} \times 15 \times 8 = \frac{1}{2} \times 120 = 60 \text{ square inches} 5. **Total area:** $$\text{Area_total} = \text{Area_rectangle} + \text{Area_triangle} = 750 + 60 = 810 \text{ square inches}$$ --- 6. **Problem 2: Find the perimeter of the L-shaped polygon (in centimeters).** 7. **Given:** All angles are right angles, side lengths 32 cm and 25 cm are labeled. 8. **Determine all side lengths:** - The L-shape has 6 sides. - Two sides are given: 32 cm and 25 cm. - The other sides can be found by subtracting overlapping lengths. 9. **Calculate missing sides:** - The vertical side adjacent to 25 cm is 32 - 25 = 7 cm - The horizontal side adjacent to 32 cm is 25 - 7 = 18 cm 10. **List all sides:** - 32 cm, 7 cm, 18 cm, 25 cm, 7 cm, 18 cm 11. **Calculate perimeter:** $$\text{Perimeter} = 32 + 7 + 18 + 25 + 7 + 18 = 107 \text{ cm}$$