The point is 13 cm from the sides of the rhombus, 12 cm from the plane, find the area if the side is 20 cm

Since the distance from point P to the sides of the rhombus is the same, point P is projected to the center of the inscribed circle, which is the intersection point of the diagonals.

The PH segment is the perpendicular to CD, the OH segment is the projection of the PH on the rhombus plane, then OH is the perpendicular to the CD.

In a right-angled triangle РOН, according to the Pythagorean theorem, OH ^ 2 = PH ^ 2 – PO ^ 2 = 169 – 144 = 25.

OH = 5 cm.

Determine the area of the triangle COD.

Sod = OH * CD / 2 = 5 * 20/2 = 50 cm2.

Then the area of the rhombus is equal to: Savsd = 4 * Ssod = 4 * 50 = 200 cm2.

Answer: The area of the rhombus is 200 cm2.