 Hi and welcome to the session. Let us discuss the following question. Question says two crossroads, each of it 10 meters, cut at right angles through the center of a rectangular park of length 700 meters and width 300 meters and parallel to its sides. Can the area of the roads also find the area of the park excluding crossroads? Give the answer in hectares. Let us now start with the solution. First of all, let us draw a simple figure to represent the given problem. Now this figure represents the given problem. Here A, B, C, D is a rectangular park and P, Q, R, S and D, F, G, H are two crossroads. Clearly we can see these crossroads intersect each other at right angles and also these crossroads are parallel to the sides of the rectangular park. Now we can write, let A, B, C, D represent the rectangular park and shaded region represent the path 10 meters wide. Now to find the area of the path, first of all we will find out areas of these two rectangles that is area of rectangle P, Q, R, S and area of rectangle E, F, G, H. Let us consider rectangle P, Q, R is. Now in this rectangle P, Q is equal to S, R is equal to 10 meters. We are given width of both the crossroads is 10 meters and P, S is equal to Q, R is equal to 300 meters. We know P, S is equal to Q, R is equal to BC. So here we can write P, S is equal to Q, R is equal to 300 meters. Now let us consider this rectangle. Now in this rectangle EF is equal to HG is equal to 700 meters. Clearly we can see EF is equal to HG is equal to length of rectangle ABCD. Now length of rectangle ABCD is 700 meters. So EF is equal to HG is equal to 700 meters and EH is equal to FG is equal to 10 meters. We know path is 10 meters wide. So EH is equal to FG is equal to 10 meters. Now we know area of a rectangle is equal to length into width. Here L represents the length of the rectangle and B represents width. Now first of all we will find out area of rectangle P, Q, R is. We know length of this rectangle is 300 meters and width of this rectangle is 10 meters. So we get area of rectangle P, Q, R is is equal to 300 multiplied by 10 meters square which is further equal to 3000 meters square. Now we will find out area of rectangle EFGH. We know length of this rectangle is 700 meters and width of this rectangle is 10 meters. So area of this rectangle is equal to 700 multiplied by 10 meters square which is further equal to 7000 meters square. Now we know width of the two roads is 10 meters. So KL is equal to LM is equal to MN is equal to KN is equal to 10 meters. Here we can write KL is equal to LM is equal to MN is equal to KN is equal to 10 meters. Now we also know that these two crossroads intersect each other at right angle. Now a quadrilateral in which all sides are equal and all angles are right angles is a square. So KLMN is a square. Now we will find out area of square KLMN below area of square is equal to side square. So area of square KLMN is equal to square of 10 which is further equal to 100 meters square. Now we know we can find area of the path or we can say we can find area of the shaded region by adding area of rectangle PQRS and area of rectangle EFGH and subtracting area of square KLMN from sum of these two areas. Clearly we can see this square is lying in this rectangle as well as in this rectangle. So we have added this area twice. So we must subtract it from sum of these two areas once. Substituting corresponding values of the areas in this expression we get area of the path is equal to 3000 plus 7000 minus 100 meters square. Now simplifying we get area of the path is equal to 9900 meters square. Now we have to represent this area in hectares we know 10,000 meters square is equal to 1 hectare. Now this implies 1 meter square is equal to 1 upon 10,000 hectares. Now this further implies 9,900 meters square is equal to 1 upon 10,000 multiplied by 9,900 hectares. Now simplifying further we get 9,900 meters square is equal to 0.99 hectares. Now we get area of the roads is equal to 0.99 hectares. Now we have to find area of the park excluding these crossroads. Clearly we can see area of the park excluding crossroads is equal to area of rectangle ABCD minus area of crossroads. Now area of the park ABCD is equal to 700 multiplied by 300 meters square. Area of the crossroads is equal to 9,900 meters square. Substituting 700 multiplied by 300 for area of rectangle ABCD and 9,900 for area of crossroads in this expression we get this expression. Now this is further equal to 210,000 minus 9,900 meters square. Now subtracting these two terms we get 2,0,0,1,0,0 meters square. Now we know 10,000 meters square is equal to 1 hectares. So 2,0,0,1,0,0 meters square is equal to 2,001,00 upon 10,000 hectares which is further equal to 20.01 hectares. So we get area of the park excluding crossroads is equal to 20.01 hectares. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.