The area of the rhombus is S = ah, where a is the side of the rhombus, h is the height of the rhombus.
AD = AH + HD = 4 + 1 = 5.
AD = AB = BC = CD (by definition of a rhombus).
Consider the triangle ABH.
ABH is rectangular (because BH is height), then by the Pythagorean theorem: AB ^ 2 = BH ^ 2 + AH ^ 2
5 ^ 2 = BH ^ 2 + 4 ^ 2
25 = BH ^ 2 + 16
BH2 = 9
Bh = 3
S diamond = AD * BH = 5 * 3 = 15
Answer: S diamond = 15
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