The angle of the parallelogram is 45 degrees, and the sides are 7√2 and 17 cm. Find its area and large diagonal.
| August 18, 2021 | education
Determine the area of the parallelogram.
Savsd = AB * AD * SinВСD = 7 * √2 * 17 * Sin45 = 119 * √2 * √2 / 2 = 119 cm2.
In a parallelogram, the sum of adjacent angles is 180, then the angle BAD = 180 – ABC = 180 – 45 = 1350.
The diagonal ВD is defined by the cosine theorem.
AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * CosABC = 98 + 289 – 2 * 7 * √2 * 17 * (- 1 / √2) = 387 + 238 = 625.
AC = 25 cm.
Answer: The parallelogram area is 119 cm2, the AC diagonal is 25 cm.
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