The area of a rhombus is calculated using the formula S = AD * BE.
The side of the rhombus is AD = AB = AE + ED = 5 + 8 = 13 cm.
The height BE is calculated using the Pythagorean theorem from the right-angled triangle BEA.
(BE) ^ 2 = (AB) ^ 2 – (AE) ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144 = 12 ^ 2.
Then, BE = 12 cm.
Substitute the values into the formula for the area of the rhombus:
S = AD * BE = 13 * 12 = 156 cm ^ 2.
Answer: the area of the rhombus is 156 cm ^ 2.
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