Question

Charlyn walks completely around the boundary of a square whose sides are each $5$ km long. From any point on her path she can see exactly $1$ km horizontally in all directions. What is the area of the region consisting of all points Charlyn can see during her walk, expressed in square kilometers and rounded to the nearest whole number?

$24$

$27$

$39$

$40$

$42$

Answer: C

Concepts:area decomposition circle area estimation

Difficulty rating: 1820

Solution:

Inside the square, Charlyn sees everything except a central square of side $5 - 2 = 3,$ an area of $25 - 9 = 16$ square kilometers.

Outside the square, the region is four rectangles each $5 \times 1$ plus four quarter circles of radius $1,$ an area of $4 \cdot 5 + \pi = 20 + \pi$ square kilometers.

The total area is $36 + \pi \approx 39$ square kilometers.

Thus, the correct answer is C.

2000 AMC 10 Problem 18

Answer: C

Difficulty rating: 1820

Solution:

Problem 18 in Other Years