As shown in the diagram, overline{ OA }& | vedclass

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Question

For the sector OACB, radius $r=35 cm$ and the measure of the angle $	heta=90(\because \overline{ OA } \perp \overline{ OB })$

Area of sector $OACB

Vedclass · Accepted Answer

$752.5$

Vedclass · Answer

For the sector OACB, radius $r=35 cm$ and the measure of the angle $	heta=90(\because \overline{ OA } \perp \overline{ OB })$

Area of sector $OACB =\frac{\pi r^{2} 	heta}{360}$

$=\frac{22}{7} 	imes \frac{35 	imes 35 	imes 90}{360}$

$=962.5 cm ^{2}$

In $\Delta AOD , \quad m \angle O =90$

$	herefore$ Area of $\Delta AOD =\frac{1}{2} 	imes OA 	imes OD$

$=\frac{1}{2} 	imes 35 	imes 12$

$=210 cm ^{2}$

Area of the shaded region

$=$ Area of sector OACB - Area of $\Delta AOD$

$=962.5-210$

$=752.5 cm ^{2}$

Thus, the area of the shaded region is $752.5 cm ^{2}$

As shown in the diagram, $\overline{ OA }$ and $\overline{O B}$ are two radii of $\odot( O , 35 cm )$ perpendicular to each other. If $OD =12\, cm ,$ find
the area of the shaded region. (in $cm^2$)

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