1. **Problem statement:** Find the areas of the two irregular polygons by splitting them into rectangles. --- ### a. First polygon 2. The polygon is a stepped shape with sides 3, 4, 2, 2, 3, 1, 3, and 4 metres. 3. We split it into two rectangles: - Rectangle 1: width = 3 m, height = 4 m - Rectangle 2: width = 2 m, height = 2 m 4. Calculate the area of each rectangle: $$\text{Area}_1 = 3 \times 4 = 12 \text{ m}^2$$ $$\text{Area}_2 = 2 \times 2 = 4 \text{ m}^2$$ 5. Total area of polygon a is the sum of the two areas: $$\text{Area}_a = 12 + 4 = 16 \text{ m}^2$$ --- ### b. Second polygon 6. The polygon is U-shaped with sides 1, 3, 3, 5, 2, and 1 metres. 7. Split it into three rectangles: - Rectangle 1 (left vertical): width = 1 m, height = 3 m - Rectangle 2 (bottom horizontal): width = 3 m, height = 1 m - Rectangle 3 (right vertical): width = 1 m, height = 5 m 8. Calculate the area of each rectangle: $$\text{Area}_1 = 1 \times 3 = 3 \text{ m}^2$$ $$\text{Area}_2 = 3 \times 1 = 3 \text{ m}^2$$ $$\text{Area}_3 = 1 \times 5 = 5 \text{ m}^2$$ 9. Total area of polygon b is the sum of the three areas: $$\text{Area}_b = 3 + 3 + 5 = 11 \text{ m}^2$$ --- **Final answers:** - Area of polygon a = $16$ m$^2$ - Area of polygon b = $11$ m$^2$