The perimeter of a rhombus is 100 cm and one of the diagonals is 40 cm. Then, the area of the rhombus in square centimeters is

perimeter of a rhombus is 100 cm

one of the diagonals is 40 cm

From the diagram

$A{O}^2+O{B}^2=A{B}^2$

$A{O}^2+{20}^2={25}^2$

$A{O}^2=625-400$

$A{O}^2=225$

$AO=15\text{cm}$

$AO=OC=15\text{cm}$

$AC=30\text{cm}$

Area of Rhombus $=\frac{1}{2}\times AC\times BD$

$=\frac{1}{2}\times 30\times 40$

$=600$