 Hello and welcome to the session. In this session we discuss the following question which says, a 90 meter by 30 meter rectangular lawn has two roads, each 3 meter wide running through its middle, one parallel to its length and the other parallel to its width, finding cost of gravelling the roads at rupees 5 per meter square. Before we move on to the solution, let's recall the formula for the area of a rectangle, and this is equal to L into B square units, L is the length of the rectangle, B is the length of the rectangle. This is the key idea for this question. Now let's proceed with the solution. Consider this figure, here this A, B, C, D is the rectangular lawn. This is of measure 90 meters by 30 meters. Now area of the rectangular lawn A, B, C, D is given by 90 into 30 meter square that is equal to 2700 meter square. Now these are the two roads running in the middle of the lawn and each road is 3 meters wide. This road that is LMNO is parallel to its length that is it's parallel to the length of the lawn and the road ESGH is parallel to the width of the lawn A, B, C, D. Now let's find out the area of LMNO, this is given by the length which is 90 into the breadth of the road which is 3 that is 90 into 3 meter square that is equal to 270 meter square. Next we find the area of ESGH this is equal to the breadth of the rectangular lawn that is 30 into the width of the road which is 3 so 30 into 3 meter square and this is equal to 90 meter square is the area of ESGH. Now clearly this area PQRS is common to both the roads so now the area of PQRS is given by 3 into 3 meter square since 3 meters is the width of the road so this is equal to 9 meter square is the area of PQRS. Now area of the roads to be graveled is equal to the area of the road LMNO plus the area of the road ESGH minus the area of the common area to the roads that is PQRS. So this is equal to now area of LMNO is 270 plus area of ESGH which is 90 minus area of PQRS which is 9 so area of roads to be graveled is equal to 270 plus 90 minus 9 meter square and this is equal to 351 meter square is the area of the roads to be graveled. Now the cost of graveling 1 meter square of road is equal to rupees 5 as given in the question. Next we find out the cost of graveling 351 meter square of road and this is equal to rupees 351 into 5 equal to rupees 1755. So the cost of graveling the roads is rupees 1755 so this is our final answer. This completes this session. Hope you have understood the solution for this question.