Q. 105.0( 4 Votes )

A circle is inscribed in APQR where mQ = 90, PQ = 8 cm and QR = 6 cm. Find the area of the blue coloured region shown in figure 13.29. (= 3.14)



Figure 13.29

Answer :

from the given figure


PQR is a right-angle triangle


PQ = 8 cm


QR = 6 cm


PR2 = PQ2 + QR2


PR2 = 82 + 62


PR = √100 = 10 cm


Radius of the incircle (r) = = = = 2 CM


area of coloured region = Area of triangle - area of circle


= × PQ × QR - π r2


= × 8 × 6 - π 22


= 24 – 12.566


= 11.433 cm2


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