1. **State the problem:** Calculate the surface area of a prism shaped like a house. 2. **Identify the prism parts:** It consists of a rectangular prism (base) and a triangular prism (roof). 3. **Rectangular prism dimensions:** Length $l=16$ cm, Width $w=5$ cm, Height $h=9$ cm. 4. **Triangular prism dimensions:** Base length $b=16$ cm, slant height $s=10$ cm, vertical height $h_t=6$ cm. 5. **Calculate the surface area of the rectangular prism:** - Area of base = $l \times w = 16 \times 5 = 80$ cm² - Area of top (under the roof) = also $80$ cm² - Area of four sides = $2 \times (l \times h + w \times h) = 2 \times (16 \times 9 + 5 \times 9) = 2 \times (144 + 45) = 2 \times 189 = 378$ cm² - Total surface area of rectangular prism without the top = base + four sides = $80 + 378 = 458$ cm² 6. **Calculate the surface area of the triangular prism (roof):** - Two triangular bases area: Each triangle area = $\frac{1}{2} \times b \times h_t = \frac{1}{2} \times 16 \times 6 = 48$ cm² - Total triangles area = $2 \times 48 = 96$ cm² - Three rectangular faces of the triangular prism: -- Two sides (slant triangle sides) with dimensions $s \times$ thickness (width of the prism) = $10 \times 5 = 50$ cm² each -- Bottom rectangle where roof meets rectangular prism = $b \times$ width = $16 \times 5 = 80$ cm² - Total rectangular faces area of roof = $50 + 50 + 80 = 180$ cm² - Total surface area of roof = triangles + rectangular faces = $96 + 180 = 276$ cm² 7. **Combine the parts:** - The rectangular prism top is replaced by the bottom rectangle of the roof, so subtract the rectangular prism top area $80$ cm² previously counted. 8. **Total surface area:** $$458 + 276 - 80 = 654 \text{ cm}^2$$ **Final answer:** The surface area of the house-shaped prism is $654$ cm².