In the parallelogram ABCD, the perpendicular KH to the line AD is drawn, and the point H

| May 6, 2021 | education

In the parallelogram ABCD, the perpendicular KH to the line AD is drawn, and the point H lies on the side AD. Find the sides, angles and area of the parallelogram, if AH = 16cm, angle A is 60, HD = 10cm.

The solution of the problem:

Angle C = angle A = 60 °;

Angle B = Angle D = 180 ° – 60 ° = 120 °.

Let’s draw a diagonal BD.
Angle ABD = angle ADB = angle A = 60 °.

The ABD triangle is equilateral.

Side AD = AB = BD = 16 + 10 = 26 cm.

Let’s omit the height of the VO.
Angle ABO = 180 ° – (90 ° + 60 °) = 30 °.

AO = AB / 2 = 26/2 = 13 cm.

BО ^ 2 = AB ^ 2 – AO ^ 2 = 26 ^ 2 – 13 ^ 2 = 676 – 169 = 507;

BО = √507 = 122.5.

Determine the area of the parallelogram.
S = AD * BO = 26 * 22.5 = 585 cm2.

Answer: the angles of the parallelogram are 60 ° and 120 °, the sides are 26 cm, and the area is 585 cm2.



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.