 Hi and how are you all today? My name is Priyanka and let us discuss this question says in a triangle ABC E is the midpoint of median AD show that area of BED is equal to one fourth the area of ABC Now for this question, let us have a figure that will help us under understanding this whole This is a triangle ABC where AD is the median of this triangle. So that means BD is equal to DC and E is the midpoint of AD that means AE is equal to ED, right? So let us start with our Solution and write down what is given to us in the question. We are given that in triangle ABC D is the midpoint or D is the midpoint but AD is Is the median E is the midpoint AD, right? So that means BD is equal to DC as well as AE is equal to ED Also, we need to prove that area of BED is equal to one fourth area of AB. Now, let us start with our proof Now, we know that in triangle ABC AD is the median. Therefore area of ABD will be equal to area of ADC that is ABD, half of this triangle will be equal to the area of half of this triangle because median of a triangle divides the triangle into triangles of equal area. Let this be the first equation. So that means since they both are half of it that means area of ABD is half of area of this full triangle. Let this be the second equation. Also, we know that in triangle E, B, D this triangle since E is the midpoint that means BE will be the median exactly. So BE is the median. So I can write down therefore area of BED is equal to area of ABE because of the same reason that is mentioned above because a median divides the triangle into two triangles of equal area. Let this be the third equation. So area of BED is equal to area of as mentioned above ABE. That implies that area of BED is half the area of ABD. Since they both are equal that means this triangle will be half of this full triangle as well as this triangle will also be half of this full triangle. That implies area of BED is equal to half. Now area of ABD, I can write as half area of ABC and this is using the first equation. So half multiplied by half will give us one by four. So area of BED is one by four area of ABC and this was the condition to be proved. So hence we have proved the given thing. I hope you enjoyed the session. Take care.