 Hi and welcome to the session. Let us discuss the following question. Question says on a square handkerchief, 9 circular designs each of radius 7 centimeters are made. Find the area of the remaining portion of handkerchief. This is the given figure 12.29. First of all let us understand that area of circle is equal to pi r square where r is the radius of the circle and area of square is equal to side square. This is the key idea to solve the given question. Now let us start with the solution. Now we know this handkerchief has 9 circular designs and radius of each circle is equal to 7 centimeters. So let us assume that radius of each circle is r. So we get r is equal to 7 centimeter. Now we know from key idea area of circle is equal to pi r square. So area of each circle is equal to pi multiplied by square of 7. So we can write area of each given circle is equal to pi multiplied by square of 7 centimeters square. Now we will substitute 22 upon 7 for pi and we get 22 upon 7 multiplied by 7 multiplied by 7 centimeter square. Now 7 and 7 will get cancelled and we get 154 centimeter square. Now we know there are 9 circular designs. So area of 9 circles is equal to 9 multiplied by 154 centimeter square. Now multiplying these two terms we get 1386 centimeter square. So area of these 9 circular designs is equal to 1386 centimeter square. Now we have to find area of remaining portion of handkerchief. If we subtract area of these 9 circular designs from complete area of square ABCD then we get area of the remaining portion of the handkerchief. So now we will find out area of square ABCD. We know area of square is equal to side square. Now we can find side AD of square ABCD by adding diameters of these 3 circles. Now we know diameter of this circle is 14 centimeters. We know diameter is twice that of radius. So radius of this circle is 7 centimeters. So diameter is equal to 2 multiplied by 7 that is 14. Now similarly diameter of this circle is 14 centimeters and diameter of this circle is also equal to 14 centimeters. So AD is equal to 14 plus 14 plus 14 centimeters. So we can write AD is equal to 14 plus 14 plus 14 centimeters which is further equal to 42 centimeters. Similarly other sides of this square are also equal to 42 centimeters. Now let us find out area of square ABCD. Now area of square ABCD is equal to square of AD and we know AD is equal to 42 centimeters. So it is equal to square of 42. Now square of 42 is equal to 1764 centimeters square. So we get area of square ABCD is equal to 1764 centimeters square. Now we know that area of remaining portion of handkerchief is equal to area of square ABCD minus area of 9 circular designs. We know area of square ABCD is equal to 1764 centimeters square and area of 9 circular designs is equal to 1386 centimeters square. So substituting their corresponding values we get area of remaining portion of handkerchief is equal to 1764 minus 1386 centimeters square. Now subtracting these two terms we get 378 centimeters square. So our required answer is area of remaining portion of the handkerchief is equal to 378 centimeters square. This completes the session. Hope you understood the solution. Take care and keep smiling.