 Hello friends, welcome to the session. I am Alka. Let's discuss the given question find the area of a rhombus if it's vertices are 3045 minus 1 4 and minus 2 minus 1 taken in order Before starting with the solution, I would like to tell you the basic idea behind the cushion now since we have to find the area of of Rhombus, which is equal to half Product of X Diagonals to find the area from us we have to find the length of the diagonals So to find the length of the diagonal we'll use the distance formula. So distance formula is Sephora given line segment a V with coordinates of a r x 1 by 1 and coordinates of vr x 2 y 2 the distance formula is square root of x 1 minus x 2 whole square plus Y 1 minus y 2 whole square So this is the distance formula for finding the length of the Diagonal now, let's start with the solution since we know that the area of Rhombus is half product of its diagonal. So first of all, we'll have to find the length of the diagonal. So length of Diagonal AC Is now here we'll use the distance formula. So it is equal to square root of x 1 minus x 2 that is 3 minus of minus 1. So it will be 3 plus 1 square plus Y 1 minus y 2 that is 0 minus 4 whole square. So this is equal to 4 4 squared is 16 plus again 4 4 squared is 16. So this is equal to Square root of 32 2. This is equal to 4 square root of 2 Units now again, we'll find the length of the diagonal BD So again, here we'll use the distance formula. So that will be equal to 4 plus 2 Whole square plus 5 plus 1 whole square This is equal to 6 squared that is 36 Again 6 squared that is 36. So this is equal to Square root of 72. This is equal to 6 square root of 2 units Now Since we have to find the area of Rhombus. So area of Rhombus Is equal to half into Product diagonals So this is equal to the length of the cos diagonal is 4 root 2 and the length of the second diagonal is 6 root 2 Here we see that This is equal to half Into 4 into 6 into 2 2 to get cancelled out and we get the area of Rhombus as 24 square units Therefore we can say that Area of Rhombus is 24 squared units. So hope you understood the solution and enjoyed the session. Goodbye and take care