Mensuration

Trapezium has ONE pair of parallel sides (a and b) and height h. Area = ½ × (a+b) × h. Think of it as: average of parallel sides × height. Common in road cross-sections, dam designs, architectural structures.

Cuboid has 6 faces: 2 pairs of (l×b), 2 pairs of (b×h), 2 pairs of (l×h). TSA = 2(lb+bh+lh). Cube: all sides = a. TSA = 6a². LSA (lateral) = 4 faces only. Cuboid LSA = 2h(l+b). Cube LSA = 4a².

Volume = space occupied inside. Cuboid: V = l×b×h. Cube: V = a³. 1 litre = 1000 cm³ = 1000 mL. 1 m³ = 1,000,000 cm³ = 1000 litres. Swimming pool volume uses cuboid formula. Cube of ice → volume of water (approximately same).

Cylinder: circular base (radius r), height h. CSA (curved) = 2πrh (like label on can). TSA = 2πr(r+h) = 2πrh + 2πr². Volume = πr²h. A tin can, pipe, well, drum are all cylinders. Volume of water in cylindrical tank = πr²h.