The perimeter of the rhombus is 32 and one of the corners is 30 °. Find the area of the rhombus.

1) Perimeter is the sum of the lengths of all sides of the figure. For a rhombus, the perimeter is equal to the sum of its four equal sides, that is, P = 4a, whence the length of the rhombus side is: a = P / 4. From the problem statement, it is known that the perimeter is 32, so a = 32/4 = 8.

2) The area of a rhombus can be found as the product of its side by the height h: S = a * h.

3) Consider a right-angled triangle, the hypotenuse is known in it, which we found in point 1 and an angle of 30 °, opposite to the height h. So h = a * sin 30 = 8 * 1/2 = 4.

4) We are looking for the area of a rhombus: S = 8 * 4 = 32.