The perimeter of the rhombus is 160 and the sine of one of the angles is three tenths. find the area of the rhombus.

All sides of the rhombus are equal, so knowing its perimeter, we find the length of the side:

a = P / 4 = 160/4 = 40.

The area of the rhombus is equal to the product of the square of the side and the sine of the angle between these sides. By condition, the sine of the angle between the sides of this rhombus is 0.3. Find the area:

S = a2 * sin α = 402 * 0.3 = 1600 * 0.3 = 480.