Find the area of a rhombus if its height is 12 cm and the smaller dioganal is 13 cm.

Since ВН is the height of the rhombus AВСD, then the ВDН triangle, in which, according to the Pythagorean theorem, we define the length of the DН leg.

DН ^ 2 = ВO ^ 2 – ВН ^ 2 = 169 – 144 = 25.

DН = 5 cm.

The AВН triangle is rectangular. Let the side AB = X cm, since the sides of the rhombus are equal, then AH = (X – DН) = (X – 5) cm.

Then, by the Pythagorean theorem: AB ^ 2 = AH ^ 2 + BH ^ 2.

X ^ 2 = (X – 5) ^ 2 + 144.

X ^ 2 = X ^ 2 – 10 * X + 25 + 144.

10 * X = 169.

X = AB = 16.9 cm.

Determine the area of the rhombus.

Savsd = AB * ВН = 16.9 * 12 = 202.8 cm2.

Answer: The area of the rhombus is 202.8 cm2.