1. **Problem Statement:** Calculate the area of the given trapezoid-like polygon with the following dimensions: - Left vertical height: 4 cm - Inner vertical height: 5 cm - Bottom segments: 2 cm, 9 cm, and 6 cm 2. **Understanding the shape:** The polygon has 5 sides with a bottom base composed of three segments totaling $2 + 9 + 6 = 17$ cm. 3. **Approach:** We can split the polygon into two trapezoids stacked vertically or use the trapezoid area formula for each part and sum them. 4. **Formula for trapezoid area:** $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two parallel sides and $h$ is the height. 5. **Calculate the area of the lower trapezoid:** - Bottom base $b_1 = 17$ cm - Top base $b_2 = 9$ cm (middle segment) - Height $h = 4$ cm $$\text{Area}_1 = \frac{(17 + 9)}{2} \times 4 = \frac{26}{2} \times 4 = 13 \times 4 = 52$$ cm$^2$ 6. **Calculate the area of the upper trapezoid:** - Bottom base $b_1 = 9$ cm - Top base $b_2 = 0$ cm (top side is a point or negligible length) - Height $h = 5 - 4 = 1$ cm $$\text{Area}_2 = \frac{(9 + 0)}{2} \times 1 = \frac{9}{2} \times 1 = 4.5$$ cm$^2$ 7. **Total area:** $$\text{Area} = \text{Area}_1 + \text{Area}_2 = 52 + 4.5 = 56.5$$ cm$^2$ **Final answer:** The area of the shape is **56.5 cm$^2$**.