The diagonals of the parallelogram are 4cm and 4√2cm, and the angle between them is 45 degrees.
| August 31, 2021 | education
The diagonals of the parallelogram are 4cm and 4√2cm, and the angle between them is 45 degrees. Find the area and perimeter.
Determine the area of the parallelogram.
Savsd = АС * ВD * Sin45 = 4 * √2 * 4 * √2 / 2 = 16 cm2.
By the cosine theorem, we determine the length of the side AB.
AB ^ 2 = OA ^ 2 + BO ^ 2 – 2 * AO * BO * Cos45 = (2 * √2) ^ 2 + 2 ^ 2 – 2 * √2 * 2 * √2 / 2 = 8 + 4 – 4 = 8.
AB = CD = √8 = 2 * √2.
Let us determine the length of the BC side.
ВС ^ 2 = OC ^ 2 + ОВС ^ 2 – 2 * OC * ОВ * Cos135 = (2 * √2) ^ 2 + 2 ^ 2 – 2 * √2 * 2 * (-√2 / 2) = 8 + 4 + 4 = 16.
BC = 4 cm.
Let’s define the perimeter. P = 2 * (AB + BC) = 2 * (2 * √2 + 4) = 8 + 4 * √2 cm.
Answer: The area is 16 cm2, the perimeter is 8 + 4 * √2 cm.
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