The acute angle of a 10cm rhombus is 20% of the obtuse angle. find the area of the rhombus.

The lengths of the sides of the rhombus are known, it is only necessary to find the sine of the angle between the sides.

The acute and obtuse angles of the rhombus are essentially adjacent – their sum is 180 °. Let’s introduce a variable.

Let m – the value of the acute angle of the rhombus, then 5 * m – the value of the obtuse angle. Let’s solve the equation:

m + 5 * m = 180;

m = 30 °.

All values are known, we find the area of the rhombus:

S = a ^ 2 * sin A = 10 ^ 2 * 1/2 = 50 cm².