Parallelogram 64414

The parallelogram has side a = 58cm and diagonals u = 89cm and v = 52cm. Calculate the perimeter and area of this parallelogram.

Correct answer:

o = 204.2836 cm
S = 2203.1082 cm²

a = 58 cm u = 89 cm v = 52 cm e = u / 2 = 89 / 2 = \frac{8 9}{2} = 44.5 cm f = v / 2 = 52 / 2 = 26 cm s = \frac{a + e + f}{2} = \frac{5 8 + \frac{8 9}{2} + 2 6}{2} = \frac{2 5 7}{4} = 64.25 cm S_{1} = s \cdot (s - a) \cdot (s - e) \cdot (s - f) = 64.25 \cdot (64.25 - 58) \cdot (64.25 - 44.5) \cdot (64.25 - 26) ≐ 550.7771 cm^{2} S_{1} = \frac{a \cdot h / 2}{2} h = 4 \cdot S_{1} / a = 4 \cdot 550.7771 / 58 ≐ 37.9846 cm u^{2} = (a + x)^{2} + h^{2} x = u^{2} - h^{2} - a = 8 9^{2} - 37.984 6^{2} - 58 = \frac{5 2 1 7}{2 3 2} ≐ 22.4871 cm x^{2} + h^{2} = b^{2} b = x^{2} + h^{2} = 22.487 1^{2} + 37.984 6^{2} ≐ 44.1418 cm o = 2 \cdot (a + b) = 2 \cdot (58 + 44.1418) = 204.2836 cm

S = a \cdot h = 58 \cdot 37.9846 ≐ 2203.1082 cm^{2} Verifying Solution: w = \frac{b + e + f}{2} = \frac{4 4 . 1 4 1 8 + 4 4 . 5 + 2 6}{2} ≐ 57.3209 cm S_{2} = w \cdot (w - b) \cdot (w - e) \cdot (w - f) = 57.3209 \cdot (57.3209 - 44.1418) \cdot (57.3209 - 44.5) \cdot (57.3209 - 26) ≐ 550.7771 cm^{2} S_{3} = 2 \cdot S_{1} + 2 \cdot S_{2} = 2 \cdot 550.7771 + 2 \cdot 550.7771 ≐ 2203.1082 cm^{2}

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