1. The area of the rhombus can be found by the formula
where
are rhombus's diagonals.
Note that then
2. The diagonals of rhombus are perpendicular and are bisectors of each other. Then the triangle formed with halfs of diagonals is right triangles with legs
The hypotenuse of this triangle is the rhombus's side. By the Pythagorean theorem
3. The distance between the point of intersection of the diagonals and the side of the rhombus is the height of right triangle considered above.
Use twice the Pythagorean theorem to find this height:
where x is projection of leg 12 cm and h is height.
Subtract the first equation from the second:
Then
Answer: