# In each picture b

The figure is shown below:

Let the side of this hexagon be “x”.

Then, in this hexagon, a total of 6 equilateral triangles can be made, which are:

ΔOED, ΔODC, ΔOCB, ΔOBA, ΔOAF, ΔOFE.

Now, in the figure given below:

In ΔOPF and ΔOPB,

POF = POB (angle in equilateral triangle = 600)

OF = OB (sides of equilateral triangle)

OP is common in both the triangles.

Hence, we can say that ΔOPF ΔOPB

Similarly, we can prove that ΔAPF Δ APB

AP = PO =

Now in, right ΔOPF,

OP2 + PF2 = OF2

b = √3x

Now,

Area of hexagon with side “x” =

Area of big triangle (green shaded) =

Probability of dot is putted in the green part

= 0.083

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Merchant of Venice (Summary and Important Questions)30 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

In each picture bKerala Board Mathematics Part-1

In each picture bKerala Board Mathematics Part-1

In each picture bKerala Board Mathematics Part-1

In each picture bKerala Board Mathematics Part-1

In each picture bKerala Board Mathematics Part-1