 Hello and welcome to the session. In this session we will see how to use problem solving strategies on geometric shapes. There are various problem solving strategies which can be used to solve any algebraic or geometrical problem like reading the problem, drawing a figure, looking for a pattern, making a simpler problem etc. Now let us consider the following example. Consider the following pattern of dots. This is the given pattern of dots and we have to draw the fourth figure using dots to continue the same pattern and we have to find the number of dots in fourth figure. Now if we look at the first figure there is one dot. In second figure a triangle is formed by adding two dots below one dot. So total number of dots here are 1 plus 2 which is equal to 3. In third figure again a triangle is formed by adding three dots below the previous figure containing three dots. So here total number of dots are 3 plus 2 plus 1 which is equal to 6. So it means we are forming triangles using a particular sequence of dots. That is we are adding a row of dots below the previous figure and the number of dots being added are in our pattern 1, 2, 3 and so on. So in the fourth place also a triangle will be formed by adding a row containing four dots below the previous figure. Let us draw it. This will be the required image at fourth place and here total number of dots will be 4 plus 3 plus 2 plus 1 that is equal to 10. Now this is the required image at fourth place with total number of dots as 10. Similarly number of dots for the image at fifth place will be 5 plus 4 plus 3 plus 2 plus 1 which is equal to 15. Now let us consider one more example where we will adopt a different strategy to find the solution. Now to solve it we first read and understand the problem. It is given that on a rectangular plot which is 20 feet wide and 40 feet long a circular pond is made of radius 7 feet. On the remaining plot it is decided to make grass bed and we have to find the area of the grass bed. Now it will be convenient if we make a figure of the given situation. So here we are using the strategy of first reading and then drawing the given situation. Let us draw it. This is a rectangular plot its width is 20 feet and length is 40 feet. To draw circular pond we draw a circle inside this rectangle. This is the circular pond inside this rectangular plot and its radius is 7 feet. Now we shade the remaining area. This remaining area is the area of the grass bed. Now from this figure it is clear that if we subtract the area of the circle from the area of rectangle we will get the remaining area that is area of grass bed. So we write area of grass bed is equal to area of rectangular plot minus area of circular pond. Now we know that area of rectangular plot will be equal to length into width minus area of circular pond. And area of circular pond will be given by pi into r square that is radius square. So this is equal to length into width that is 40 into 20 minus. Now we know the value of pi is 22 upon 7 into radius square and radius is given as 7. So we have 7 into 7 and this is equal to 40 into 20 is 800 minus 22 into 7 that is 154. So this is equal to 646. So we can say that area of grass bed is equal to 646 square feet. Thus we can use various strategies to solve a problem. This completes our session. Hope you enjoyed this session.