Q. 44.0( 4 Votes )
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
Area of hexagon with side “x” =
Area of big triangle (green shaded) =
Probability of dot is putted in the green part
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