Question

A circle is inscribed in an equilateral triangle. A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
about 60%

about 50%

about 30%

about 75%

Answer 1

Answer:

The correct answer is first option 60%

Step-by-step explanation:

The radius of a circle is inscribed in an equilateral triangle with side a = a/2√3

To find the area of equilateral triangle

Here side be 'a'

Area of equilateral = √3a²/4

To find the area of circle

Here radius = a/2√3

Area = πr²

 = π(a/2√3)

 = 3.14a²/12

To find the probability

probability = area of circle/area of triangle

   = 3.14a²/12/ √3a²/4

   = 3.14/3√3

   = 0.6043 ≈ 60.43 %  60 %

The correct answer is first option 60%