1. **State the problem:** Find the surface area of the composite L-shaped figure made of two rectangular prisms joined perpendicularly. 2. **Identify dimensions:** - Bottom horizontal prism: length $=10$ in, width $=2$ in, height $=2$ in. - Vertical prism: width $=2$ in, depth $=2$ in, height $=8$ in. 3. **Formula for surface area of a rectangular prism:** $$SA = 2(lw + lh + wh)$$ 4. **Calculate surface area of each prism separately:** - Bottom prism: $$SA_1 = 2(10 \times 2 + 10 \times 2 + 2 \times 2) = 2(20 + 20 + 4) = 2(44) = 88$$ - Vertical prism: $$SA_2 = 2(2 \times 2 + 2 \times 8 + 2 \times 8) = 2(4 + 16 + 16) = 2(36) = 72$$ 5. **Calculate the overlapping area where prisms join:** The overlapping face is $2$ in by $2$ in, so area is: $$A_{overlap} = 2 \times 2 = 4$$ 6. **Calculate total surface area of composite figure:** $$SA = SA_1 + SA_2 - 2 \times A_{overlap} = 88 + 72 - 2 \times 4 = 160 - 8 = 152$$ 7. **Final answer:** The surface area of the composite figure is **152 in$^2$**.