Determine the length of the sides of the rhombus.
AB = BC = CD = AD = AH + DH = 56+ 36 = 92 cm.
In a right-angled triangle СDН, according to the Pythagorean theorem, we determine the length of the leg СН.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 92 ^ 2 – 56 ^ 2 = 8464 – 3136 = 5328.
BH = √5328 = 12 * √37cm.
Determine the area of the rhombus.
Savsd = АD * BН = 92 * 12 * √37 = 1104 * √37 cm2.
Answer: The area of the rhombus is 1104 * √37 cm2.
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