Find the perimeter and area of the rhombus if its side is 13 cm and one of the diagonals is 24 cm.

Given: rhombus ABSD
AB = 13 cm, diogagal AS = 24
Find: RAVSD – ?, SABSD-?
Decision :
The sides of the rhombus are equal, which means AB = BC = SD = HELL = 13cm
The intersection point of the dioganals is -O
Consider a triangle ABO, in which AB = 13 cm, VO = 12 cm (the diagonal is halved by the intersection point)
Find AO by the Pythagorean theorem
AB squared = BO squared + AO squared
AO squared = AB squared – BO squared
AO squared = 13 in sq. -12 in sq.
AO in kv = 169-144 = 25
AO = 5 cm
CB = 5 • 2 = 10
Sabcd = 1/2 • 10 • 24 = 120 cm
Rabsd = 13 • 4 = 52 cm
Answer: The area of the rhombus is 120 cm
The perimeter is 52 cm