Question

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In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. Find the area of the remaining portion of the triangle.​

Answer 1

I hope it may help u

Answer 2

First calculate area of equilateral triangle that is √3a^2/4
√3×24^2/4=249.4

lets draw median to all sides we know that in equilateral triangle all median intersects at incenter so it give us some clue to find radius of circle
we know that median bisects each other in ratio 2:1
so,
It needed to find height of triangle to go further
1/2×24×h=√3×24^2/4

h=20.78
so,h can be divide in ratio 2:1
that is,
2x+x=20.78
x=6.92 so the ratio
13.85:6.92
so radius is 6.92
Area of circle 22/7×6.92^2=150.5
Area of remaining part =area of triangle - area of circle=249.4-150.5=98.9(approx.)

You can solve it in any method
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