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

In a rhombus, all sides are equal AB = BC = CD = AD;
AD = AH + HD = 5 + 8 = 13;
AB = AD = 13;
Since the triangle ABH is right-angled, by the Pythagorean theorem we find the height of the BH:
BH = √ (AB²-AH²) = √ (13²-5²) = √169-25 = √144 = 12;
Let’s find the area of the rhombus S = BH * AD = 12 * 13 = 156.
Answer: Area of a rhombus ABCD = 156.