Q. 105.0( 4 Votes )

# A circle is inscribed in APQR where m∠Q = 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

PR^{2} = PQ^{2} + QR^{2}

PR^{2} = 8^{2} + 6^{2}

PR = √100 = 10 cm

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

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

= × PQ × QR - π r^{2}

= × 8 × 6 - π 2^{2}

= 24 – 12.566

= 11.433 cm^{2}

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Gujarat Board Mathematics

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Figure 13.29

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Figure 13.27

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figure 13.26.

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figure 13.25

Gujarat Board Mathematics