Question
Tue February 15, 2011 By: Dhatshana K

Find the area of the shaded region

Expert Reply
Wed March 23, 2011

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

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