One side of a rhombus is 20 mm, and the longer diagonal is 32 mm. What is the area of the rhombus?

Remember that the diagonals of a rhombus are perpendicular bisectors of each other.

So, one side of the rhombus, half the longer diag and half the shorter diag form the 3 sides of a right triangle
with the rhombus side being the hypotenuse.

In this case, let the shorter diagnoal be x mm. In the right triangle,

Hypotenuse = 20
One side = 32/2 = 16
Other side = x/2

Applying Pythagoras principle,

 (taking only the positive square root)

So the shorter diagonal = 12*2 = 24 mm

Area of the rhombus is given by the formula (1/2)*d1*d2 where d1, d2 are the 2 diagonals.

Here, the area = (1/2)*32*24 = 32*12 = 384 sq mm

:)