Question

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?

Answer 1

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]