Question

Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is in the hexagon.

Answer 1

Answer:

0.26

Step-by-step explanation:

Given :

To find the probability that a point on rectangle lies inside the hexagon

Solution :

Probability of an event = $\frac{Number \ of \ favourable \ outcomes}{Total \ number \ of \ possible \ outcomes}$

⇒ $\frac{Area \ of \ Hexagon}{Area \ of \ Rectangle}$

As, we can split a regular hexagon into 6 equilateral triangle of same length,

Area of hexagon

= 6 × Area of equilateral triangle of length 2 cm

= $6 \times \frac{\sqrt{3}}{4} \times (2)^2 = 6\sqrt{3}$ sq.cm

⇒ $\frac{6\sqrt{3}}{5\times8}=\frac{3\sqrt{3}}{20}$ ≈ 0.26