Find the area of the shaded region

Asked by Dhatshana | 15th Feb, 2011, 01:03: PM

Expert Answer:

Dear Student,

 Here is the answer.

 

Let the outer square be ABCD, of 14cm each side.

Areas of this square=14x14= 196 Sq. CM .............. (i)

 

As there is a gap of 3 cm from each of the wall, hence it becomes another square (EFGH), each side of (14-3-3=) 8 cm.

 

Since there are semicircles within this EFGH, it makes another internal square (IJKL), each side of (8-2-2=) 4 cm.

 

Hence area within non-shaded portion = area of square IJKL of each side of 4 cm + 4 semicircle of dia 4 cm each

                                                =  4x4 + 4x(3.14 x 2x2 /2)

                                                = 16 + 25.12= 41.12 Sq Cm ....... (ii)

 

Hence area of shaded portion = (i) – (ii) = 196-41.12

Hence area of shaded portion= 154.88 Sq. Cm

 

Regards

Team Topperlearning

Answered by  | 23rd Mar, 2011, 12:24: PM

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