1. **Problem Statement:** Find the area of the composite figure consisting of a rectangle and a triangle on its right side. 2. **Formulae and Rules:** - Area of a rectangle: $$\text{Area} = \text{length} \times \text{width}$$ - Area of a triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Given Dimensions:** - Rectangle: length = 12 ft, width = 7 ft - Triangle: base = 5 ft, height = 8 ft 4. **Calculate the area of the rectangle:** $$\text{Area}_{\text{rectangle}} = 12 \times 7 = 84 \text{ ft}^2$$ 5. **Calculate the area of the triangle:** $$\text{Area}_{\text{triangle}} = \frac{1}{2} \times 5 \times 8 = \frac{1}{2} \times 40 = 20 \text{ ft}^2$$ 6. **Calculate the total area of the composite figure:** $$\text{Total Area} = 84 + 20 = 104 \text{ ft}^2$$ --- 1. **Problem Statement:** Find the area of the shaded region inside the pentagon formed by the given sides and a diagonal. 2. **Given Dimensions:** - Pentagon sides: top = 5 in, right = 6 in, bottom = 3 in, left = 2 in - The shaded region excludes a small triangle at the bottom-left corner formed by the diagonal. 3. **Approach:** - Calculate the area of the entire pentagon by dividing it into simpler shapes. - Subtract the area of the small triangle excluded from the shaded region. 4. **Calculate the area of the pentagon:** Assuming the pentagon can be split into a rectangle and two triangles or trapezoids, but since exact shape details are missing, approximate by dividing into a rectangle (top side 5 in by height estimated from sides) and triangles. 5. **Calculate the area of the small triangle excluded:** - Base = 2 in (left side) - Height = unknown, but assuming height matches the vertical distance from bottom to top side. Since exact height is not given, we cannot compute exact area without more data. **Final answers:** - Area of composite figure (rectangle + triangle): **104 ft²** - Area of shaded region in pentagon: **Insufficient data to calculate exact area**