Composite Area Ead249

1. **State the problem:** We need to find the area of a composite figure composed of rectangles and a triangle. 2. **Analyze the figure:** The figure consists of: - A vertical rectangle on the left with width $3$ in and total height $15$ in. - A top-left slanted triangular section. - A horizontal rectangle extending to the right from the middle with length $9$ in and height $2$ in. 3. **Identify dimensions:** - The vertical rectangle height is $15$ in. - The lower left interior vertical segment is $4$ in, so the top vertical segment of the left rectangle is $15 - 4 = 11$ in. - The top horizontal portion is $7$ in. - The horizontal rectangle has length $9$ in and height $2$ in. - The right end vertical side of the horizontal rectangle is $2$ in. 4. **Calculate areas of parts:** - **Left vertical rectangle:** $$\text{Area} = \text{width} \times \text{height} = 3 \times 15 = 45 \text{ in}^2$$ - **Top-left triangle:** The triangle is formed by the top horizontal segment of length $7$ in and vertical height $4$ in (the lower interior vertical segment). $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 4 = 14 \text{ in}^2$$ - **Horizontal rectangle:** $$\text{Area} = \text{length} \times \text{height} = 9 \times 2 = 18 \text{ in}^2$$ 5. **Sum all areas:** $$\text{Total area} = 45 + 14 + 18 = 77 \text{ in}^2$$ 6. **Final answer:** The area of the figure is **77 square inches**.