Chapter 14, Problem 18RP

To determine

To find the area enclosed by the locus of the moving point.

Answer to Problem 18RP

  $(33+4\pi )\text{ sq inch}$

Explanation of Solution

Given:

The point outside the square $3$ units on a side moves so that it is always $2$ units from the square.

Calculation:

The area enclosed by the locus of the moving point can be found as follows-

Area of $K=3\times 3=9\text{sqcm}$

Area of A $=$ Area of B $=$ Area of C $=$ Area of D $=3\times 2=6\text{ sq}\text{. cm}$

Net area of A,B,C,D $=4\times 6=24\text{ sq}\text{. cm}$

Area of one fourth of the circle of radius $2$ cm $=\frac{1}{4}\pi {(2)}^2=\pi \text{ sq}\text{. inch}$

Total area $=4\times$ Area of one fourth of the circle $=4\pi \text{ sq inch}$

So, the area of locus

  $\begin{array}{l}=(24+9+4\pi )\\ =(33+4\pi )\text{ sq inch}\end{array}$