1. **Problem statement:** Find the area of the cross section and the volume of each prism. --- **a) Rectangular prism with dimensions 5 cm (width), 2 cm (height), and 9 cm (length):** 1. Area of cross section = width \times height = $5 \times 2 = 10$ cm$^2$. 2. Volume = cross-sectional area \times length = $10 \times 9 = 90$ cm$^3$. --- **b) Triangular prism with triangle base sides 8 m each and height 9 m:** 1. The cross section is an equilateral triangle with side length 8 m. 2. Area of equilateral triangle = $\frac{\sqrt{3}}{4} \times 8^2 = \frac{\sqrt{3}}{4} \times 64 = 16\sqrt{3}$ m$^2$. 3. Volume = cross-sectional area \times length (height of prism) = $16\sqrt{3} \times 9 = 144\sqrt{3}$ m$^3$. --- **c) Rectangular prism with cross section 12 mm (length) and 2 mm (height), prism length 6 mm:** 1. Area of cross section = $12 \times 2 = 24$ mm$^2$. 2. Volume = $24 \times 6 = 144$ mm$^3$. --- **d) Prism with rectangular face 9 cm by 5 cm and slant height 10 cm:** 1. Area of cross section = $9 \times 5 = 45$ cm$^2$. 2. Volume = cross-sectional area \times length = $45 \times 10 = 450$ cm$^3$. --- **Final answers:** a) Area = 10 cm$^2$, Volume = 90 cm$^3$ b) Area = $16\sqrt{3}$ m$^2$, Volume = $144\sqrt{3}$ m$^3$ c) Area = 24 mm$^2$, Volume = 144 mm$^3$ d) Area = 45 cm$^2$, Volume = 450 cm$^3$