Q4 of 18 Page 70

In each picture below, the explanation of the green part is given. Calculate in each, the probability of a dot put without looking to be within the green part.

A triangle got by joining alternate vertices of a regular hexagon.


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


More from this chapter

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2

In each picture below, the explanation of the green part is given. Calculate in each, the probability of a dot put without looking to be within the green part.

A square with all vertices on a circle.


 3

In each picture below, the explanation of the green part is given. Calculate in each, the probability of a dot put without looking to be within the green part.

Circle exactly fitting inside a square.


 5

In each picture below, the explanation of the green part is given. Calculate in each, the probability of a dot put without looking to be within the green part.

A regular hexagon formed by two overlapping equilateral triangles.


 1

Rajani has three necklaces and three pairs of earrings, of green, blue and red stones. In what all different ways can she wear them? What is the probability of her wearing the necklace and earrings of the same colour? Of different colours?