A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/4 #, and the triangle's area is #32 #. What is the area of the triangle's incircle?

1 Answer
Binayaka C.
Aug 19, 2016

Area of triangle's incircle #=17.25(2dp)# sq.unit

Explanation:

#/_A=pi/2=90^0;/_B=pi/4=45^0 ;/_C=180-(90+45)=45^0#This is an isocelles right angled triangle #AB=AC:.1/2*AB*AC=1/2*AB^2=32or AB^2=64or AB=8;AC=8; BC=sqrt(8^2+8^2)=sqrt128=11.31 #Semi perimeter : #s=(8+8+11.31)/2=13.655#
Incircle radius: #r=A_t/s=32/13.655=2.343:.#Area of triangle's incircle : #A_c=pi* 2.343^2=17.25(2dp)#sq.unit[Ans]

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