 Hello and welcome to the session. In this session we will discuss areas. First let's recall the formula for the area of different plain closed figures like we know that area of a rectangle is equal to length into the breadth of the rectangle. Then we have area of a square is equal to side of the square into side of the square that as you can see the side square. Then next we have area of a triangle this is equal to half into base into height then next is area of a parallelogram is equal to the base into height then we have area of a circle is equal to pi into radius square. Next we have area of a trapezium consider this trapezium A B C D in which we have that A B is parallel to C D and A B is of length A and C D is of length B and the distance between these two parallel sides is H. So we have area of the trapezium A B C D is equal to half into the sum of the parallel sides into the perpendicular distance between the two parallel sides. So we write area of trapezium is equal to half into sum of the parallel sides into the perpendicular distance between the parallel sides. Now let us consider this trapezium A B C D where we are given that A B is of length 5 cm, C D is of length 3 cm and the distance between the two parallel sides A B and C D is 2 cm. So we have area of trapezium A B C D is equal to half into the sum of the two parallel sides that is 3 plus 5 into the distance between the two parallel sides which is 2. This is equal to half into 8 into 2 this is equal to 8 cm square is the area of the trapezium A B C D. Next formula that we consider is area of a general quadrilateral consider this general quadrilateral A B C D this can be split into two triangles by drawing one of its diagonals. So as you can see we have drawn the diagonal AC. Now we have drawn the perpendicular from the point B and D on the diagonal AC and these perpendicular are of length H1 and H2. Now this diagonal AC divides this quadrilateral A B C D into two triangles triangle AC D and triangle A B C. So area of the quadrilateral A B C D is equal to area of triangle A C D plus the area of triangle A B C and we already know how we find the area of a triangle. So on doing this we get the formula for the area of a general quadrilateral which is equal to half into D into H1 plus H2 where you know that H1 H2 are the lengths of the perpendicular from the two vertices of the quadrilateral on the diagonal AC of the quadrilateral A B C D and this D is the length of the diagonal AC. So this is the formula that we use to find the area of a general quadrilateral. Consider quadrilateral A B C D in which we have the lengths of the perpendicular as 2.5 centimeters and 1.5 centimeters that is you can say that H1 is equal to 2.5 centimeters and H2 is equal to 1.5 centimeters and the length of the diagonal AC is equal to 6 centimeters that is we have D is equal to 6 centimeters. So now area of the quadrilateral A B C D is equal to half into D that is 6 into H1 plus H2. This is equal to half into 6 into 4 which is equal to 12 centimeters square. Next we have area of a rhombus. Consider this rhombus A B C D now it's diagonal AC device it into two triangles triangle A C D and triangle A B C. So we say that area of the rhombus A B C D is equal to area of triangle A C D plus area of triangle A B C. On doing this we get the area of a rhombus is equal to half into D1 into D2 that is you can say that half into product of its diagonal that is we have that D1 and D2 are the lengths of the diagonals of the rhombus like for this rhombus A B C D we have AC is equal to 6 centimeters B D is equal to 4 centimeters that is we have D1 is 6 centimeters and D2 is 4 centimeters so the area of the rhombus A B C D is equal to half into D1 into D2 which is equal to 12 centimeters square. In the same way we can find the area of any polygon by dividing it into triangles for example let's consider this pentagon A B C D E we shall now construct its diagonals we have drawn its two diagonals AC and EC so these two diagonals divide this pentagon A B C D E into three triangles triangle A EC triangle B EC and triangle ABC so we have that the area of the pentagon A B C D E is equal to the sum of the areas of its triangles that is area of triangle A EC plus area of triangle D EC plus area of triangle ABC we have also drawn the perpendicular of length H1 H2 H3 on the diagonals EC and AC of the pentagon A B C D E so that we can easily find the area of the three triangles so this completes the session hope you have understood how we find the area of different plain closed figures