 Hello and welcome to the session. In this session, we discussed the following question which says, in the given figure, A B C D is a quadrilateral, a line through D parallel to AC meets B C produced in P, prove that area of triangle A B P is equal to area of quadrilateral A B C D. Before moving on to the solution, let's recall the fact that says that two triangles on the same base or equal basis and between the same parallel are equal in area. This is the key idea for this question. Now we move on to the solution. This is the figure given to us. We are given that A B C D is a quadrilateral. Then it's also given to us that a line through D is parallel to AC, that is we have B P is parallel to AC. And we need to prove that area of triangle A B P is equal to the area of quadrilateral A B C D. Consider the triangles AC D and triangle AC P they lie on the same base AC and between the same parallel, that is we have AC is parallel to D P. So triangle AC D and triangle AC P lie on the base AC and between the same parallel AC and D P. Now since we know that triangles on the same base and between the same parallel are equal in area, therefore we say that area of triangle AC D is equal to the area of the triangle AC P. Now adding area of triangle A B C on both sides we get area of triangle AC D plus area of triangle A B C is equal to area of triangle AC P plus area of triangle A B C. Now from the figure you can see that area of triangle AC D plus area of triangle A B C gives us area of the quadrilateral A B C D and this is equal to area of triangle AC P plus area of triangle A B C which is given by area of triangle A B P. So we have now proved that area of triangle A B P is equal to the area of the quadrilateral A B C D so hence proved this completes the session hope you have understood the solution for this question.