Question: Q 5 A 10 l B 10 m 11 2 m The figure shows two rectangular blocks joined side by side, with block A as a long horizontal cuboid in the lower center-left and block B as a taller cuboid on the upper center-right; the label A is on the lower block and B is on the upper block. position_hint=top-left, center what is the total surface area of the composite shape

1. **State the problem:** Calculate the total surface area of the composite shape formed by two rectangular blocks A and B joined side by side. 2. **Identify dimensions:** - Block A: length $10$, width $l$ (not given explicitly, assume $l=2$ for calculation as per block B's width), height $2$ (assumed from block B's height difference). - Block B: length $10$, width $m=11$, height $2$. 3. **Formula for surface area of a cuboid:** $$SA = 2(lw + lh + wh)$$ where $l$ = length, $w$ = width, $h$ = height. 4. **Calculate surface area of block A:** Assuming $l=10$, $w=2$, $h=2$ (since block B is taller, height of A is 2): $$SA_A = 2(10 \times 2 + 10 \times 2 + 2 \times 2) = 2(20 + 20 + 4) = 2(44) = 88$$ 5. **Calculate surface area of block B:** Given $l=10$, $w=11$, $h=2$: $$SA_B = 2(10 \times 11 + 10 \times 2 + 11 \times 2) = 2(110 + 20 + 22) = 2(152) = 304$$ 6. **Calculate the area of the joined face:** The blocks are joined side by side along a face of dimensions $10 \times 2$: $$Area_{joined} = 10 \times 2 = 20$$ 7. **Calculate total surface area of composite shape:** $$SA_{total} = SA_A + SA_B - 2 \times Area_{joined} = 88 + 304 - 2 \times 20 = 392 - 40 = 352$$ 8. **Final answer:** The total surface area of the composite shape is $$\boxed{352}$$ square units.