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Question

In given frame (shaded region), the length and breadth of inner rectangle PQRS are 4 cm and 2 cm respectively, find the area of the frame if width of the frame is 2 cm throughout.
  1. 24 cm2
  2. 32 cm2
  3. 40 cm2
  4. 48 cm2


Solution

The correct option is C 40 cm2
In rectangle PQRS
PQ = SR = 4 cm,  PS = QR = 2 cm
In rectangle ABCD
AB = CD = 4+2+2 = 8 cm
BC = AD = 2+2+2 = 6 cm

Area of the frame = Area of the rectangle ABCD - Area of the rectangle PQRS
Area of rectangle ABCD = AB × BC
                                        = 8 × 6
                                        = 48 cm2
Area of rectangle PQRS = PQ × QR
                                        = 4 ×
                                        = 8 cm2
Hence Area of the frame = 48 - 8 
                                         = 40 cm2

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