two adjacent side of a parallelogram are of length 5 cm and 7 cm and the diagonal connecting the end of this side of length 9cm find area of parallelogram
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Put Heron's formula to get the area of one half of the parallelogram. Semiperimeter equals (5+7+9)/2 = 21/2 cm. Let a = 5, b = 7, c =9. s-a = 11/2, s-b = 7/2, s-c = 3/2. As per the formula, area of the triangle = sqrt{s(s-a)(s-b)(s-c)} = 21sqrt(11)/2 for one half. So the total area equals 21sqrt(11) cm^2.
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