Q. 44.0( 4 Votes )

# In each picture b

Answer :

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 = 60^{0})

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,

OP^{2} + PF^{2} = OF^{2}

⇒

⇒

⇒

⇒

⇒ 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 :

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