Q. 474.4( 7 Votes )

In the given figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region. [Use √3 = 1.73 and π = 3.14.]


Answer :

Here we will draw median from all the vertices of the equilateral triangle and the point at which they intersect will be the incircle of the triangle and that will be the centre of the circle. Thenwith the help of which we will find out the height of the triangle and subsequently the radius of the circle and ultimately the area of the shaded region (region of equilateral triangle excluding the area of circle inscribed).



As AD = BF = CE = h


Consider ∆ADB, ADB = 90°, BD = 6 cm



122 = AD2 + 62 (putting the given values)


144 = AD2 + 36


144 – 36 = AD2


AD2 = 108






We also know that a point O will divide each median in a ratio of 2:1






Area of the circle = πr2



Area of the circle = 12π cm2 eqn1






Area of shaded region = area of triangle – area of circle



Area of the shaded region = (36×1.73) – (12×3.14)


Area of the shaded region = 62.28 -37.68


Area of the shaded region = 24.6 cm2



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
RD Sharma | Area of Sector and SegmentRD Sharma | Area of Sector and SegmentRD Sharma | Area of Sector and Segment61 mins
RD Sharma |  Area of Sector and SegmentsRD Sharma |  Area of Sector and SegmentsRD Sharma | Area of Sector and Segments25 mins
Throwing the Light on Area of SectorThrowing the Light on Area of SectorThrowing the Light on Area of Sector43 mins
Champ Quiz | Area Related with the CircleChamp Quiz | Area Related with the CircleChamp Quiz | Area Related with the Circle45 mins
Surface Area and VolumeSurface Area and VolumeSurface Area and Volume49 mins
Surface Area and VolumesSurface Area and VolumesSurface Area and Volumes43 mins
Areas Related to CircleAreas Related to CircleAreas Related to Circle36 mins
RD Sharma | Imp Concepts : Surface Area And VolumesRD Sharma | Imp Concepts : Surface Area And VolumesRD Sharma | Imp Concepts : Surface Area And Volumes43 mins
RD Sharma | Imp. Qs. From Surface Area And VolumesRD Sharma | Imp. Qs. From Surface Area And VolumesRD Sharma | Imp. Qs. From Surface Area And Volumes47 mins
Quiz | Surface Area and VolumesQuiz | Surface Area and VolumesQuiz | Surface Area and Volumes42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses