 Hi and welcome to the session. Let us discuss the following question. Question says, construct the following quadrilateral. We have to construct quadrilateral ABCD in which AB is equal to 4.5 centimeters, BC is equal to 5.5 centimeters, CD is equal to 4 centimeters, AD is equal to 6 centimeters and AC is equal to 7 centimeters. Let us now start with the solution. Now first of all, we will draw a rough sketch of quadrilateral ABCD. Now this figure represents the rough sketch of quadrilateral ABCD. Now we are given that AB is equal to 4.5 centimeters, BC is equal to 5.5 centimeters, CD is equal to 4 centimeters, AD is equal to 6 centimeters and AC is equal to 7 centimeters. Now note that all the four sides of quadrilateral ABCD are known and we also know the length of diagonal AC. Now to construct this quadrilateral ABCD, we need to construct two triangles, triangle ABC and triangle ADC both on opposite sides of diagonal AC. Let us now start with the construction. Now first step of construction is draw AC equal to 7 centimeters. Now to construct quadrilateral ABCD, we need to locate two more points that is point B and point D. Now first of all we will locate point B. To locate this point, we will draw an arc of radius 4.5 centimeters from center A and another arc of radius 5.5 centimeters from center C. The point of intersection of two arcs will represent point B. So second step of construction is with AR center draw an arc of radius 4.5 centimeters. Now clearly you can see we have drawn an arc of radius 4.5 centimeters from center A. Now third step of construction is with CA center draw an arc of radius 5.5 centimeters to intersect the previous arc at point B. Now this is a arc of radius 5.5 centimeters which has been drawn from center C. Now it is intersecting the previous arc at point B. Now we will locate the point D. To locate this point we will draw an arc of radius 6 centimeters from center A and another arc of radius 4 centimeters from center C. And the point of intersection of two arcs will be point D. So next step of construction is with AR center draw an arc of radius 6 centimeters opposite to B with reference to line AC. Now clearly you can see this is an arc of radius 6 centimeters drawn from center A. Now next step of construction is with CA center draw an arc of radius 4 centimeters to intersect the previous arc at point D. Now clearly you can see this is an arc of radius 4 centimeters drawn from center C. Now these two arcs intersect each other at point D. To obtain quadrilateral ABCD we need to join AB, BC, CD and DA. So next step of construction is join AB, BC, CD and DA. Now we have joined AB, BC, CD and DA. So ABCD is the required quadrilateral where AC is equal to 7 centimeters, AB is equal to 4.5 centimeters, BC is equal to 5.5 centimeters, CD is equal to 4 centimeters and DA is equal to 6 centimeters. So this is our required construction. This completes the session. Hope you understood the solution. Take care and have a nice day.