Composite Area Aee2Db

1. **State the problem:** We need to find the area of a composite figure that looks like a trapezoid and can be decomposed into two triangles and one rectangle. 2. **Formula used:** The area of a rectangle is given by $$\text{Area} = \text{length} \times \text{width}$$ and the area of a triangle is $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$. 3. **Decompose the figure:** The figure can be split into: - A rectangle in the middle - A triangle on the left side - A triangle on the right side 4. **Calculate the rectangle area:** Suppose the rectangle has length $b$ and height $h$. 5. **Calculate the triangles' areas:** Each triangle has a base and height that can be measured from the grid. 6. **Sum all areas:** Total area = area of rectangle + area of left triangle + area of right triangle. 7. **Example with grid values:** - Bottom edge length (rectangle base) = $8$ - Rectangle height = $3$ - Left triangle base = $2$, height = $3$ - Right triangle base = $2$, height = $3$ 8. **Calculate each area:** - Rectangle area = $8 \times 3 = 24$ - Left triangle area = $\frac{1}{2} \times 2 \times 3 = 3$ - Right triangle area = $\frac{1}{2} \times 2 \times 3 = 3$ 9. **Total area:** $$24 + 3 + 3 = 30$$ **Final answer:** The area of the composite figure is $30$ square units.