Find the corners of the rhombus if its height is 4 cm and the perimeter is 32 cm.

A rhombus is a quadrilateral with all sides and opposite angles equal.
ABCD – rhombus, BH = 4 cm – height, AB + BC + CD + AD = 4x = 32 cm.
Find the length of the rhombus side:
4x = 32;
x = 32/4;
x = 8.
Consider the BHA triangle: BH = 4 cm and HA – legs, AB = 8 cm – hypotenuse, BHA angle = 90 degrees. Since the ВН leg is 2 times smaller than the hypotenuse AB, it lies opposite an angle equal to 30 degrees (properties of a right-angled triangle), therefore, the HAB angle (angle A) = 30 degrees.
Since the opposite angles in the rhombus are equal, the angle A = angle C = 30 degrees.
By the theorem on the sum of the angles of a quadrangle:
angle A + angle B + angle C + angle D = 360 degrees;
30 + x + 30 + x = 360;
2x = 360 – 60;
2x = 300;
x = 300/2;
x = 150.
Angle B = Angle D = 150 degrees.
Answer: angle A = angle C = 30 degrees, angle B = angle D = 150 degrees