Question

A man is running around a regular hexagonal field of side length 6m, so that he can always at a distance 3m from the nearest boundary. Find the length of path travelled by him in one round

Answer 1

Answer:

Hence, the length of the fence required all around it is 260 m. 7. ... So the distance covered can be found from the perimeter = 2 ( L + B) ... Perimeter = 6 × side of the regular hexagon.

Step-by-step explanation:

Answer 2

Given:

side of hexagonal$=6m$

distance of the man from the nearest boundary$=3m$

To find: the length of the path travelled by the man in one round.

Solution:

Understand that from the given question, the man runs such that he is always at 3m from the boundary. so at the corners of the hexagon, he will be covering an arc and then in a straight line along the length of the hexagon.

Draw the required figure.

Observe that at the corners of the hexagon a sector of $\[{60^ \circ }\]$ is formed, since, there are 6 corners so 6 sectors will be formed of $\[{60^ \circ }\]$ each if we combine all the six sectors a circle can be formed of radius 3 m.

Therefore, the circumference of the circle/ or the distance travelled by the man at the corners of the hexagon is,

$\[\begin{array}{l} = 2\pi r\\ = 2 \times \frac{{22}}{7} \times 3\\ = \frac{{132}}{7}\\ = 18.85m\end{array}\]$

Find the length travelled by the man.

length travelled by the man $=$ no. of the sides of the hexagon $\[ \times \]$ length of one side of the hexagon + distance travelled at the corners of the hexagon.

$\[\begin{array}{l} = 6 \times 6 + 18.85\\ = 36 + 18.85\\ = 54.85m\end{array}\]$

Hence, the length travelled by the man is $54.85m$.