Дано : ABCD - параллелограмм, угол CDE = 45 градусов, MD = 4, BM = 6, BM пренадлежит AD, найти площадь abcd

To find the area of the parallelogram ABCD, we can use the formula A = base * height.

First, let's find the height of the parallelogram. Since ABCD is a parallelogram, the opposite sides are parallel and have the same length. Therefore, the height of the parallelogram is the distance between AD and BC.

Since BM is a height of the parallelogram, we can use it to find the length of AD. From the given information, we know that BM = 6. Since BM belongs to AD, we can divide AD into two parts: AM and MD. Since MD = 4, we have AM = AD - MD = 6 - 4 = 2.

Now we have the length of BC = AM = 2.

To find the length of the other base, we can use the given angle CDE = 45 degrees and the fact that CD is parallel to BM. Since BM = CD, we have angle BMD = 45 degrees. This means that the triangle BMD is an isosceles right triangle.

Using trigonometry, we can find the length of BD: tan(45 degrees) = BM / BD. Substituting the given value, we have tan(45 degrees) = 6 / BD. Solving for BD, we have BD = 6 / tan(45 degrees) = 6.

Now we have the length of both bases: BC = 2 and BD = 6.

Finally, we can find the area of the parallelogram ABCD: A = base * height = BC * BD = 2 * 6 = 12.

Therefore, the area of parallelogram ABCD is 12.