JAMB 1988 · UME · Q34

A quadrant of a circle of radius 6 cm is cut away from each corner of a rectangle 25 cm long and 18 cm wide. Find the perimeter of the remaining figure.

Worked solution (try it first)
  1. Each corner cut takes 6 cm off both sides that meet there.
  2. The straight edges left are 2(25−12)+2(18−12)=26+12=382(25 - 12) + 2(18 - 12) = 26 + 12 = 38 cm.
  3. Each corner now has a quarter-circle arc of radius 6.
  4. Four quarters make a full circle: 2π×6=12π2\pi \times 6 = 12\pi cm.
  5. Perimeter =(38+12π)= (38 + 12\pi) cm, option B.

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