 Hello and welcome to the session. In this session we will discuss area of parallelograms and triangles. Basically, area of a figure is a number in some unit associated with the part of the plane enclosed by that figure and if we have that a and b are congruent figures then area of the figure a which is represented by a r a is equal to area of the figure b. Also if a planar region formed by a figure t is made up of two non-overlapping planar regions formed by figures a and q then we have area of the figure t is equal to area of the figure p plus area of the figure q. We know that two congruent figures have same area but the converse is not true that is two figures with equal areas need not be congruent. Next we have figures on the same base and between the same parallel. Now two figures are said to be on the same base between the same parallel they have a common base or a side and the vertices or the vertex the common base of each figure lie on a line parallel to the base. Like if you consider this figure in this triangle pdc and trapezium abcd lie on the same base dc between the same parallel ab and cd and it is very important that out of the two parallels one must be the line containing the common base. As in this case out of the two parallel ab and cd cd is the common base. Next we discuss parallelograms on the same base and between the same parallel like in this figure we have two parallelograms parallelogram abcd and parallelogram escd which is on the same base dc and between the same parallel af and dc. Let's try and find out a relation between the areas of two parallelograms on the same base and between the same parallel. We see that the parallelograms on the same base and between the same parallel are equal in area that is in this figure we get that the area of the parallelogram abcd is equal to the area of the parallelogram escd and the converse of this statement can be written as parallelograms on the same base or equal basis and having equal areas lie between the same parallel and basically the area of a parallelogram is the product of its any side and the corresponding altitude like the area of the parallelogram abcd is given by its side ab multiplied by its corresponding altitude that is d e. If we have a parallelogram and a triangle are on the same base and between the same parallel then we have area of triangle is half the area of parallelogram like in this figure we have the parallelogram abcd and triangle dec are on the same base dc and between the same parallel ab and dc then in this case we have area of the triangle dec is equal to half of the area of the parallelogram abcd. Next we discuss triangles on the same base and between the same parallel like in this figure we have two triangles triangle abc and triangle pbc on the same base bc and between the same parallel ap and bc we find that two triangles on the same base or equal basis between the same parallel are equal in area like for this figure we have area of triangle abc is equal to area of the triangle pbc converse of this statement can be given as two triangles having the same base equal basis and equal areas lie between the same parallel we know that area of triangle is equal to half the product of its base or any side and the corresponding altitude so from this formula of the area of triangle we can say that two triangles with same base equal basis and equal areas equal corresponding altitudes we have an important result according to which we have that a median of a triangle divides it into two triangles of equal areas suppose that abc is a triangle and ab is its median so we can say that area of triangle abd is equal to area of the triangle acd this completes the session hope you understood the concept of areas of parallelograms and triangles