equilateral triangle inscribed in a circle high or altitude = 48 cm find the area of the shaded region area of the circle area of equilateral triangle circumference of circle perimeter of triangle

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equilateral triangle inscribed in a circle high or altitude = 48 cm find the area of the shaded region area of the circle area of equilateral triangle circumference of circle perimeter of triangle

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Answer:

Correct option is C)

Area of circle =48π

⇒πr

2

=48π

⇒r=

48

=4

3

units

Now, ON⊥BC. So, ON is the height of △OBC correspoding to BC.

Area of △ABC = Area △OBC + Area △OCA + Area △OAB

4

3

a

2

=3×area△OBC=3×

2

1

×BC×ON

4

3

a

2

=3×

2

1

×a×r=3×

2

1

×0×4

3

4

3

a

2

=

2

3

×4

3

×a

⇒a=24

∴ Perimeter of equilateral △ABC=3a=3×24=72 units

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