 Hi friends I am Purva and today we will discuss the following question. Triangle ABC is isosceles with AB is equal to AC is equal to 7.5 centimeter and BC is equal to 9 centimeter. The height AD from A to BC is 6 centimeter. Find the area of triangle ABC what will be the height from C to AB that is CE and we are given this figure. Let us now begin with the solution. Now we are given AB is equal to 6 centimeter and BC is equal to 9 centimeter and we have to find the area of this triangle ABC. So we have area of triangle ABC is equal to half into base into height. Now here we have BC as base and AD as height. So we have that is area of triangle ABC is equal to half into BC into AD. Now this is equal to half into we are given BC is equal to 9 centimeter. So we have 9 into and we are given AD is equal to 6 centimeter. So we have 6. Canceling 2 in denominator and numerator we get 3 in numerator. So we have this is equal to 9 into 3 is 27. So we get 27 centimeter square. So we get area of triangle ABC is 27 centimeter square. Now we have to find the length of CE. Now again in this triangle ABC if we take AB as base then we have CE as height. So we have also area of triangle ABC is equal to half into base that is AB into height that is CE that is we have. Now area of triangle ABC is equal to 27 centimeter. So we have 27 is equal to half into now we are also given that AB is equal to 7.5 centimeter. So we have 7.5 into CE and this implies 27 into 2 upon 7.5 is equal to CE. Now solving this we get this implies CE is equal to 7.2 centimeter. So we have found the length of CE to be 7.2 centimeter. Thus we write our answer as area of triangle ABC is equal to 27 centimeter square and length of CE is equal to 7.2 centimeter. Hope you have understood the solution. Bye and take care.