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in Areas Related To Circles by (65.5k points)

In the Figure given below, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.

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(i) Each side of square ABCD =14 cm. 

∴ Area of square ABCD 

= (Side)2 

= (14)2 

= 196 sq.cm. 

(ii) Measure of radii of 4 circles, r = \(\frac{14}{2}\) = 7 cm. 

∵ Distance between tangents which touches circles externally, 

d = R + r = 7 + 7 = 14 cm. 

Area of segment with centre, 

A = ? r = 7 cm, θ = 90°

∴ Total area of 4 sectors 

= 4 × 38.5 = 154 sq.cm. 

(iii) The Area of track : 

= (Area of GHIJ – Area of ABCD) 

= 196 – 154 

= 42 sq.cm.

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