 Hello and welcome to the session. In this session we discussed the following question which says A, V, C, D is a pentagon in which E, G drawn parallel to D, A means V, A produced at G and C, F drawn parallel to D, V means A, V produced at F. Show that area of the pentagon A, V, C, D, E is equal to area of triangle D, G, F. First let's recall the fact which says that two triangles on the same base 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. In this we have that A, B, C, D, E is a pentagon. A, B, C, D, E is a pentagon. Then we are also given that E, G is drawn parallel to D, A and C, F is drawn parallel to D, B. We need to prove that area of the pentagon A, B, C, D, E is equal to the area of triangle D, G, F. Now look at the triangles D, B, C and D, B, F. These two triangles are on the same base D, B between the same parallel C, F and D, B. Since it's given to us that C, F is parallel to D, B, therefore using the key idea we say that area of the triangle D, B, C is equal to the area of the triangle D, B, F. Let this be equation one. Now look at the triangles A, D, E and A, D, G. These two triangles are on the same base A, D between the same parallel E, G, D, A. Since E, G is parallel to D, A, therefore using the key idea we say that area of the triangle A, D, E is equal to the area of the triangle A, D, G. Let this be equation two. Next adding equations one and two we get area of the triangle D, B, C plus the area of the triangle A, D, E is equal to the area of the triangle D, B, F plus the area of the triangle A, D, G. Next adding area of the triangle A, B, D on both sides we get area of triangle D, B, C plus area of triangle A, D, E plus area of triangle A, B, D is equal to area of triangle D, B, F plus area of triangle A, D, G plus area of triangle A, B, D. Now from the figure you can see that area of triangle D, B, C plus the area of triangle A, D, E plus the area of triangle A, B, D is given by area of the pentagon A, B, C, D, E. This is equal to area of triangle D, B, F plus area of triangle A, D, G plus the area of triangle A, B, D and this is given by the area of the triangle B, G, F. And here suppose you prove this only that area of the pentagon A, B, C, D, E is equal to area of triangle D, G, F. So hence proved. So this completes the session. Hope you have understood the solution for this question.