Paper 2 rarely gives you a plain circle. It gives you a shape built from a rectangle and a semicircle, or a circle cut out of a square, or a path running round a pond. The method never changes: break the figure into pieces you already know, work out each piece, then add or subtract. Two traps recur. For area, decide whether the pieces are being joined (add) or one is being removed from the other (subtract). For perimeter, only walk round the OUTSIDE — any edge where two pieces meet is inside the shape and does not count.
Worked example
Problem A shape is made up of a rectangle 20 cm by 14 cm with a semicircle of diameter 14 cm joined to one of its shorter sides. Take π = 22/7. Find its area and its perimeter.
The semicircle sits on the 14 cm side, so its diameter is 14 cm and its radius is 14 ÷ 2 = 7 cm.
Rectangle: 20 × 14 = 280 cm². Semicircle: whole circle 22/7 × 7 × 7 = 154, then halve it, 154 ÷ 2 = 77 cm².
Area = 280 + 77 = 357 cm².
For the perimeter, the curved edge is π × r = 22/7 × 7 = 22 cm. Walk round the outside: 20 + 14 + 20 + 22 = 76 cm.
Watch out The 14 cm side where the semicircle joins the rectangle is INSIDE the shape. It counts once for the area calculation and not at all for the perimeter.