1. **State the problem:** We need to find the area of the trapezoid with sides 6.4 cm (top), 7.6 cm (bottom), 4.2 cm (left vertical), and 4.4 cm (right diagonal), with a right angle at the bottom-left corner. 2. **Recall the formula for the area of a trapezoid:** $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two parallel sides (bases), and $h$ is the height (the perpendicular distance between the bases). 3. **Identify the bases and height:** - Bases: top side $b_1 = 6.4$ cm, bottom side $b_2 = 7.6$ cm - Height $h$ is the vertical side on the left, $h = 4.2$ cm (since there is a right angle, this side is perpendicular to the bases). 4. **Calculate the area:** $$\text{Area} = \frac{(6.4 + 7.6)}{2} \times 4.2$$ 5. **Simplify inside the parentheses:** $$6.4 + 7.6 = 14$$ 6. **Substitute and simplify:** $$\text{Area} = \frac{14}{2} \times 4.2 = 7 \times 4.2$$ 7. **Multiply:** $$7 \times 4.2 = 29.4$$ **Final answer:** The area of the trapezoid is $29.4$ square centimeters.