 hey friends so now we are going to deal with the problem solving on herons formula what is herons formula herons formula is nothing but a formula herons formula is nothing but a formula given or which is used to find out the area of triangle which with three sides given and the formula looks like this s times s minus a times s minus b times s minus c where a b and c are the side lengths side length side length of a triangle okay so let's now do the sum it says find the area of a triangle very good two sides of which are 8 centimeter and 11 centimeter so hence it's given a is equal to let's say 8 centimeter and b is let's say 11 centimeter two sides are given c is not known but other information given which is perimeter is 32 centimeter what is perimeter so if you have a triangle like this so perimeter is let's say this is side a this is a b and b and this is c so perimeter is given by perimeter p is a plus b plus c right so hence from here this from this information you can find out c so that means p is equal to a plus b plus c so hence c is equal to p minus a minus b which is equal to 32 minus 8 minus 11 which is equal to 13 centimeter is it so hence what did we find out the third side is now known to us now simply deployment of formula and finding out the result what is s s is p upon 2 semi-perimeter that means a plus b plus c by 2 now perimeter was already given and that was equal to 32 isn't it so hence it will be 32 upon 2 which is 16 centimeter right so what is the area of the triangle now before you find out the you know the area you it's better to find out all the values separately so hence s is now known now let's find out s minus a so s minus a is 16 minus 8 which is 8 centimeter s minus b is 16 minus 11 which is 5 centimeter and s minus c is 16 minus 13 which is 3 centimeter yep so these are the three sides so 8 5 and 3 are the three sides now so hence the area of the triangle area of the given given triangle will be equal to under root write the formula s minus a s minus b s minus c which is equal to under root 16 into 8 into 5 into 3 and now your factorization skills will come to play so let's see let's try to factorize this prime factor is it so it is 2 to the power 4 into 2 to the power 3 into 5 into 3 so now we can pull off some powers of 2 isn't it so we can say 2 to the power 6 into 2 into 5 into 3 can we say that yes we can say that so hence this is nothing but 2 to the power 3 times under root 2 into 5 into 3 which is 30 so hence area is 8 root 30 centimeter squared by centimeter squared area unit will be meter squared or centimeter square or inch square or you know any dimension of length square so since the values were given in centimeter so hence the unit is centimeter square please do not forget to mention the units is that okay so this is how you have to find out the area if the sides are given so now the learning is in this in this case it was not a direct question that means all the three sides were not given but an extra information of perimeter was given so you have to use that information to find the find the third side and then find the triangles area okay so hence you know you should be knowing the meaning of perimeter to solve this question