A circle is inscribed in triangle ABC, AB=AC=15cm, BC=24 cm. Calculate: (i). The radius of incircle (ii). The area of the shaded region. [Take π= 3.14]
Answers
Answer:
RADIUS OF INCIRCLE = 4 cm
AREA OF SHADED REGION = 57.72 cm^2
Step-by-step explanation:
HEY THERE, HERE IS YOUR SOLUTION< HOPE IT HELPS>
semi perimeter(s)= (15+15+24)÷2=27 cm-------1)
area(a)=√s(s-a)(s-b)(s-c)
⇒√27×12×12=√81×144
⇒9×12=108 cm^2-------2)
now we can say area of triangle ABC could also be equal to =
⇒ar(AOC)+ar(BOC)+ar(AOB)=108 cm^2
⇒1/2(15×r)+1/2(15×r)+1/2(24+r)=108 cm^2
⇒15r/2+15r/2+12r=108 cm^2
⇒54r/2=108 cm^2
∴r⇒(108×2)÷54= 4CM
NOW area of shaded region = (area of triangle) -(area of circle)
⇒108- πr^2=108-(22/7×16)
⇒108-50.28=57.72 cm^2
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Answer:
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