 Hello and welcome to the session. Let us discuss the following question. It says Ratha made a picture of an aeroplane with colored paper as shown in figure. Find the total area of the paper used. Let us now move on to the solution. Now to find the area of the paper used we need to find the area of the five figures 1, 2, 3, 4 and 5. So we first find the area of the first figure which is a triangle. Actually it is an isocellous triangle right? So the area of the first figure which is a triangle is given by the Heron's formula which is s into s minus a into s minus b into s minus c where a plus b plus c by 2 and here a is 1 centimeter. If this is 1 centimeter then this is also 1 centimeter, 5 centimeter and c is also 5 centimeter. So s is 5 plus 5 plus 1 upon 2 that is 5.5. So the area of first figure is equal to under the root of s which is 5.5 into s minus a that is 5.5 minus 1 into 5.5 minus b into and here b is 5 into s minus c that is 5.5 minus 5 and this is equal to under the root of 5.5 into 4.5 into 0.5 into 0.5 and this is equal to 2.6 approximately. Now we find the area of the second figure which is a parallelogram. So area of second figure is equal to the area of the parallelogram and area of the parallelogram is given by base into height. Now here base of the parallelogram is 1 centimeter and the height is 6.5 centimeter. So it is 1 centimeter into 6.5 centimeter. So the area is 6.5 centimeter square and here also we need to write the unit of the area which is centimeter square. Now we see that figure 4 and figure 5 dimensions. So we find the area of figure 4 which is a triangle and it is a right angle triangle. So its area is given by 1 by 2 into base into height. Now here base is 1.5 centimeter and height is 6 centimeters. So the area is 1 by 2 into 1.5 centimeter into 6 and this is equal to 4.5 centimeter square which is same as area of the figure 5. Now we have to find the area of figure 3 which is a trapezium. Now to find the area of the trapezium we divide the trapezium into two figures and for that we draw a line parallel to this line since we want to form a parallelogram. So this is also 1 centimeter. So we have divided a trapezium into two figures. One is a parallelogram the other is a triangle. Now this length is 1 centimeter and since this is a parallelogram opposite sides are equal and parallel. This is 1 centimeter this is 1 centimeter and if this is 1 centimeter this length is also 1 centimeter and since this much is 1 centimeter so the remaining is also 1 centimeter because the total length is 2 centimeter. So the remaining length is 1 centimeter. Let's name these two areas as A and B. So the area of figure 3 is equal to area which is a parallelogram plus area. Now we see that figure B is an equilateral triangle figure B which is an equilateral triangle having sides as 1 centimeter is given by root 3 by 4 into A is 1 centimeter. So the area becomes root 3 by 4 into 1 centimeter square which is equal to root 3 by 4 centimeter square which is equal to 0.433 centimeter square approximately. Now the area of the triangle is also given by the formula 1 by 2 into base into height. So this implies this area is equal to 1 by 2 into base into the height and this implies height is equal to 0.433 into 2 upon base. Now here the base of this equilateral triangle has length 1 centimeter. So this becomes 0.433 into 2 upon 1 centimeter which is equal to 0.866 centimeter. So the height of this triangle is 0.866 centimeter which is same as the height of the parallelogram. Now we have to find area of figure A which is a parallelogram which is given by the formula base into height. Now here base is 1 centimeter and height is 0.866 centimeter which becomes 1 centimeter into 0.866 centimeter. So the area of figure A is 0.866 centimeter square. Now area of figure 3 is area of A plus area of B. Now area of B is 0.433 centimeter square let's call this as 1. Area of parallelogram that is figure A is 0.866 centimeter square approximately let's call this as 2. Now area of figure 3 is equal to 1 plus 2. Now that is area of B plus area of A area of B is 0.33 centimeter square and 2 is the area of A which is 0.866 centimeter square. So the area of the figure 3 is 1.3 centimeter square approximately. Now the area of figure used is equal to area of figure 1 plus figure 2 plus figure 3 plus figure 4 plus figure 5. Now area of figure 1 is 2.6 centimeter approximately area of figure 2 is 6.5 centimeter square approximately and area of figure 4 and 5 are equal which is 4.5 centimeter square and the area of figure 3 is 1.3 centimeter square. So let's substitute all these values and this is equal to 19.4 centimeter square approximately hence the area of the paper used is 19.4 centimeter square approximately and this completes the question. Bye for now take care have a good day.