In parallelogram ABCD with sides of 12 cm and 20 cm, the diagonals intersect at point O, with AO = 6

| September 27, 2021 | education

In parallelogram ABCD with sides of 12 cm and 20 cm, the diagonals intersect at point O, with AO = 6, BO = 7, the angles are 30 degrees and 150 degrees. Find the perimeter of the parallelogram, diagonals, and angles.

The task of using the following properties of a parallelogram:

the diagonals are halved by the intersection point;
the smaller diagonal lies opposite the acute angle, the larger one opposite the obtuse one;
opposite angles are equal;
P = 2 * (a + b).
1) AO = 6 cm, then AC = 12 cm,

2) BO = 7 cm, then BD = 14 cm,

3) ∟В = ∟ D = 30˚,

4) ∟А = ∟С = 150 ˚,

5) P = 2 * (12 + 20) = 2 * 32 = 64 (cm).

If you do not dig deeper, then the problem is solved, but, it should be noted that the condition was drawn up incorrectly, because in ∆ ABD the largest angle A and opposite to it must lie the largest side BD. However, in this triangle the largest side is AB.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.