1. **State the problem:** Find the area of the given Y-like polygon with a V-shaped notch. 2. **Analyze the shape:** The polygon can be divided into simpler shapes to calculate the area. We have a large polygon with height 21 m, top-left horizontal segment 4.5 m, top-right horizontal segment 12 m, left slanted side 16 m, and bottom horizontal segment 5 m. 3. **Approach:** We split the polygon into two trapezoids and one triangle (the notch). Calculate each area and subtract the notch area. 4. **Calculate the area of the large trapezoid:** The trapezoid has bases 4.5 m and 12 m, and height equal to the vertical distance between these bases. Since the total height is 21 m and the bottom segment is 5 m, the height of the trapezoid is $21 - 5 = 16$ m. Area trapezoid = $\frac{(b_1 + b_2)}{2} \times h = \frac{(4.5 + 12)}{2} \times 16 = \frac{16.5}{2} \times 16 = 8.25 \times 16 = 132$ m$^2$. 5. **Calculate the area of the bottom rectangle:** The bottom horizontal segment is 5 m and the height is 5 m (since total height is 21 m and trapezoid height is 16 m). Area rectangle = $5 \times 5 = 25$ m$^2$. 6. **Calculate the area of the notch (triangle):** The notch is a V-shaped cut near the top center. Assume the notch is an isosceles triangle with base equal to the difference between the top-right and top-left segments: $12 - 4.5 = 7.5$ m. The height of the notch is the difference between the left slanted side and the trapezoid height: $16 - 16 = 0$ m, but since the notch is near the top, we consider the height as the vertical distance from the top to the notch base, which is not given explicitly. Without explicit height, assume the notch area is negligible or zero. 7. **Calculate total area:** Total area = Area trapezoid + Area rectangle - Area notch Since notch area is negligible, total area = $132 + 25 = 157$ m$^2$. **Final answer:** $$\boxed{157 \text{ m}^2}$$