Keep on walking

Geometry Level 3

Kishore walks completely around the boundary of a square field whose sides sre $5$ km each.From any point on his path,he can see exactly $1$ km in all directions.Find the area of the region Kishore can see during his walk.

$\textbf{Details and Assumptions}$

If the answer is expressible in the form $(a+\pi)$ where $a$ is a natural number,then find $a$ .

$\textbf{Hints}$

Sketch the diagram carefully.

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The answer is 36.

2 solutions

Brock Brown
Feb 5, 2015

To simplify the problem, we can write a diagram and make the task to find the shaded area:

diagram diagram

To simplify the problem even further, we can notice that the shaded area consists of four sections that look like this:

smaller diagram

We can now easily calculate the area of this shape and multiply it by 4 to arrive at the final answer:

implication

Were you using a HB (#2) pencil ? Just curious.

Venture HI - 6 years, 4 months ago

Sure was! A #2 Ticonderoga, to be specific. A classic, reliable writing utensil.

Brock Brown - 6 years, 4 months ago

I can't understand your 2nd fig. Can you please explain aggain in better view. ?

darshan parmar - 6 years, 4 months ago

Sure.

Better? Better?

I darkened the line around the shape so you can understand where figure 2 comes from. The area of figure 2 can be found by adding the areas of the 2km×4km region, the 1km×1km region, and the area of the quarter circle which can be found with (1÷4)×π. Just multiply the area of figure 2 by 4 and there's your answer.

Brock Brown - 6 years, 4 months ago

Write a comment or ask a question...

Venture HI - 6 years, 4 months ago

Navneel Mandal
Feb 28, 2015

Mandal!!! Loved this question!! Awesome!!

First of all thanks!Nextly, tumi ki ekjon bangali? $\smile$

Anik Mandal - 6 years, 3 months ago

Keep on walking

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The answer is 36.

2 solutions

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