1. **Problem Statement:** Determine the perimeter and area of the composite polygon with sides 5 in, 6 in, 7 in, 10 in, and 15 in. 2. **Understanding the Shape:** The shape consists of a trapezoid and two right-angled rectangles stacked on the right. 3. **Perimeter Calculation:** The perimeter is the sum of all outer side lengths. 4. **Area Calculation:** To find the area, break the shape into simpler parts: trapezoid and rectangles. 5. **Formula for Trapezoid Area:** $$\text{Area} = \frac{1}{2} (b_1 + b_2) h$$ where $b_1$ and $b_2$ are the lengths of the two parallel sides and $h$ is the height. 6. **Formula for Rectangle Area:** $$\text{Area} = \text{length} \times \text{width}$$ 7. **Steps to Solve:** - Identify the bases and height of the trapezoid. - Calculate the trapezoid area using the formula. - Calculate the areas of the rectangles. - Sum all areas to get the total area. 8. **Important:** Make sure to use consistent units and carefully identify which sides correspond to which parts of the shape. 9. **No final numeric answer is provided as per your request.** If you want, I can guide you through each calculation step by step.