a circle is inscribed in an equilateral triangle having side 24cm, if the circle's area cut from the triangle, then find the remaining area of the triangle.
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Answered by
0
Answer:
area of triangle -area if circle
Answered by
2
Answer:
HOPE IT HELPFUL
Step-by-step explanation:
Let ABC be an equilateral triangle of side 24cm, and let AD be perpendicular from A on BC. Since the triangle is equilateral, so AD bisects BC
∴ BC=CD=12cm
The center of the inscribed circle will coincide with the centroid of △ABC.
∴ OD=
3
AD
In △ABD, we have
AB
2
=AD
2
+BD
2
[Using Phythagoras Theorem]
⇒24
2
=AD
2
+12
2
⇒AD=
24
2
−12
2
=
(24−12)(24+12)
=
36×12
=12
3
cm.
OD=
3
1
AD=(
3
1
×12
3
)cm=4
3
cm
Area of the incircle=π(OD)
2
=[
7
22
×(4
3
)
2
]cm
2
=[
7
22
×48]cm
2
=150.85cm
2
Area of the triangle ABC=
4
3
(side)
2
=
4
3
(24)
4
=249.4cm
2
∴ Area of the remaining portion of the triangle
=(249.4−150.85)cm
2
=98.55cm
2
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