1. **State the problem:** Calculate the total surface area of the frustum formed by cutting a right pyramid ABCD with a plane EXOH parallel to the base. 2. **Given data:** - Base rectangle ABCD with AB = 32 cm, BC = 24 cm - Scale height of original pyramid = 44 cm - EF = 8 cm, FG = 6 cm (segments on the frustum top) 3. **Understanding the frustum:** The frustum is formed by slicing the pyramid parallel to the base at some height, creating a smaller similar rectangle on top. 4. **Calculate the scale factor for the top rectangle:** The original base dimensions are AB = 32 cm and BC = 24 cm. The top rectangle segments EF = 8 cm and FG = 6 cm correspond to the scaled dimensions. 5. **Find the scale factor $k$:** $$k = \frac{EF}{AB} = \frac{8}{32} = 0.25$$ Check with FG and BC: $$\frac{FG}{BC} = \frac{6}{24} = 0.25$$ So, scale factor $k = 0.25$. 6. **Calculate the height of the frustum:** Original height $H = 44$ cm. Height of smaller pyramid above the frustum $h = k \times H = 0.25 \times 44 = 11$ cm. Height of frustum $H_f = H - h = 44 - 11 = 33$ cm. 7. **Calculate areas:** - Area of base rectangle $A_1 = AB \times BC = 32 \times 24 = 768$ cm$^2$. - Area of top rectangle $A_2 = EF \times FG = 8 \times 6 = 48$ cm$^2$. 8. **Calculate the slant height $l$ of the frustum:** The frustum is a truncated pyramid with rectangular bases. The difference in half-lengths: $$\Delta a = \frac{32 - 8}{2} = 12$$ $$\Delta b = \frac{24 - 6}{2} = 9$$ Slant height: $$l = \sqrt{H_f^2 + \Delta a^2 + \Delta b^2} = \sqrt{33^2 + 12^2 + 9^2} = \sqrt{1089 + 144 + 81} = \sqrt{1314} \approx 36.26$$ cm. 9. **Calculate lateral surface area:** Perimeter of base $P_1 = 2(32 + 24) = 112$ cm. Perimeter of top $P_2 = 2(8 + 6) = 28$ cm. Lateral surface area $A_L = \frac{(P_1 + P_2)}{2} \times l = \frac{112 + 28}{2} \times 36.26 = 70 \times 36.26 = 2538.2$ cm$^2$. 10. **Calculate total surface area:** $$A_{total} = A_1 + A_2 + A_L = 768 + 48 + 2538.2 = 3354.2$$ cm$^2$. 11. **Final answer:** Total surface area of the frustum to the nearest whole number is **3354 cm$^2$**.