1. **State the problem:** We need to find the area of a barn wall composed of a rectangle and a trapezoid on top. 2. **Identify the shapes and dimensions:** - Rectangle: height $11$ ft, base $15$ ft. - Trapezoid on top: height $4$ ft, bottom base $15$ ft, top base shorter by two right triangles of base $3$ ft each on the sides. 3. **Calculate the top base of the trapezoid:** The total base is $15$ ft. Each side has a right triangle with base $3$ ft cut off, so the top base is: $$15 - 3 - 3 = 9 \text{ ft}$$ 4. **Calculate the area of the rectangle:** $$\text{Area}_{\text{rectangle}} = \text{height} \times \text{base} = 11 \times 15 = 165 \text{ ft}^2$$ 5. **Calculate the area of the trapezoid:** Formula for trapezoid area: $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1 = 15$ ft (bottom base), $b_2 = 9$ ft (top base), and $h = 4$ ft. Calculate step-by-step: $$\text{Area}_{\text{trapezoid}} = \frac{(15 + 9)}{2} \times 4 = \frac{24}{2} \times 4 = 12 \times 4 = 48 \text{ ft}^2$$ 6. **Calculate total area of the barn wall:** $$\text{Area}_{\text{total}} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{trapezoid}} = 165 + 48 = 213 \text{ ft}^2$$ **Final answer:** The area of the barn wall is $213$ square feet.