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.

• A. 24 $c{m}^2$
• B. 32 $c{m}^2$
• C. 40 $c{m}^2$
• D. 48 $c{m}^2$

Answer 1

The correct option is C 40 $c{m}^2$

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 $\times$ BC
= 8 $\times$ 6
= 48 cm${}^2$
Area of rectangle PQRS = PQ $\times$ QR
= 4 $\times$ 2
= 8 cm${}^2$
Hence Area of the frame = 48 - 8
= 40 cm${}^2$