 Hello friends, let's discuss the following question. It says a field is in the shape of trapezium whose parallel sides are 25 meter and 10 meter. The non-parallel sides are 14 meter and 13 meter. Find the area of the field. Now to find the area of this field which is in the shape of trapezium will divide the trapezium into a triangle and a parallelogram. For that you drop a perpendicular from B to the line CD and also from B we draw a line parallel to AD to form a parallelogram AB ED. Let's call this point as E and this is M. So let us now move on to the solution. The area of the field is equal to the area of triangle BEC plus area of parallelogram AB ED. BE parallel to AD therefore BE is equal to AD that is 13 meter. So in triangle BEC BC is 14 meter and EC is 15 meter since AB is parallel to DE therefore BE is 10 meter and AB ED is a parallelogram therefore the opposite sides are equal and hence AB is equal to DE which is 10 meter therefore EC will be 15 meter BE is equal to 13 meter which is equal to AD. Now we'll find the area of triangle BEC by Heron's formula for that we need to find S which is A plus B plus C by 2 where A is 14, B is 15, C is 13 upon 2 it is equal to 21. Now the area of triangle BEC where the Heron's formula is given by S into S minus A into S minus B into S minus C and this is equal to 21 into 21 minus 14 into 21 minus 15 into 21 minus 13 and this is equal to root 21 into 7 into 6 into 8 simplifying this we have 7 into 3 into 2 into 2 taking them out of root is equal to 84 since the unit of length is given to be in meter so the area is having unit meter square now we have to find area of parallelogram AED ED is equal to base into height of the parallelogram is given by N is a perpendicular to DC but AM is equal to BM so we need to find BM now we know that the area of triangle is equal to 84 meter square and the area of triangle is given by 1 by 2 it is BM that is 1 by 2 into base which is 15 meter into the height BM so this implies T4 meter square is equal to 1 by 2 into 15 BM is equal to you can find the area of the parallelogram ABED which is equal to base into height now base is D height is AN now DE is parallel to AB so DE is equal to AB which is 10 meter into 2 upon 15 meter this becomes equal to 112 meter square so the area of feet is equal to area of triangle BEC which is 84 meter square plus area of parallelogram which is 112 meter square so total area is 196 meter square hence the answer is 196 meter square so this completes the question hope you enjoyed this session goodbye and take care