Job Recruitment Website - Ranking of immigration countries - There is a point O in the quadrilateral ABCD, and the length of the vertical line from O to the four sides is 5cm. The perimeter of the quadrilateral is 18cm, and the area of the quadrilateral is squa

There is a point O in the quadrilateral ABCD, and the length of the vertical line from O to the four sides is 5cm. The perimeter of the quadrilateral is 18cm, and the area of the quadrilateral is squa

There is a point O in the quadrilateral ABCD, and the length of the vertical line from O to the four sides is 5cm. The perimeter of the quadrilateral is 18cm, and the area of the quadrilateral is square centimeters. Connect O and the four vertices of the quadrilateral and divide the quadrilateral into four parts. Let the sides of the quadrilateral be A, B, C and D (where a+b+c+d= 18), then the areas of each small triangle are 5a/2, 5b/2, 5c/2 and 5d/2 respectively.

So the area of the quadrilateral is 5a/2+5b/2+5c/2+5d/2 = 5 (a+b+c+d)/2 = 5x18/2 = 45.