The height BH of the rhombus ABCD divides its side AD into segments AH = 5 and HD = 8. Find the area of the rhombus.

Find the area of a rhombus if AH = 5 and ND = 8
Solution: BP side is equal to the sum of AH and HD: 5 + 8 = 13
Since in a rhombus all sides are equal, then AB = BC = CD = AD = 13
The area of a rhombus is equal to the product of its side by the height drawn to it
S = CH * AD
VN can be found by the Pythagorean theorem, since triangle ABH is rectangular (BH is height)
BH (leg) = root of AB ^ 2 – AH ^ 2 = root of 13 ^ 2 – 5 ^ 2 = root of 169-25 = root of 144 = 12
S = 12 * 13 = 156 square units
Answer: 156 sq. Units