1. **State the problem:** We need to find the area of the shaded part, which consists of two identical parallelograms joined along their longer base inside a rectangle. 2. **Identify given dimensions:** The total width of the rectangle is 20 cm, with two vertical segments of 5 cm each on the sides, and the total height is 32 cm. 3. **Determine the base and height of one parallelogram:** Since the two parallelograms are joined along their longer base, the combined base length is 20 cm minus the two 5 cm segments on the sides, so the base of each parallelogram is: $$\text{Base of one parallelogram} = \frac{20 - 2 \times 5}{2} = \frac{20 - 10}{2} = \frac{10}{2} = 5\text{ cm}$$ 4. **Height of the parallelogram:** The height is the total height of the rectangle, which is 32 cm. 5. **Formula for the area of a parallelogram:** $$\text{Area} = \text{base} \times \text{height}$$ 6. **Calculate the area of one parallelogram:** $$\text{Area}_1 = 5 \times 32 = 160\text{ cm}^2$$ 7. **Calculate the total shaded area (two parallelograms):** $$\text{Total area} = 2 \times 160 = 320\text{ cm}^2$$ **Final answer:** The area of the shaded part is **320 cm\textsuperscript{2}**.