In the rectangle ABCD AD = 10 cm, AB = 12 cm. Through the middle K of the side BC, a perpendicular MK

| February 7, 2021 | education

In the rectangle ABCD AD = 10 cm, AB = 12 cm. Through the middle K of the side BC, a perpendicular MK is drawn to its plane, equal to 5 cm. Calculate: a) the distance from point M to line AD; b) the area of the triangle AMB and its projection onto the plane of this triangle; c) the distance between the lines BM and AD.

The distance from point M to line AD is the perpendicular MH drawn to side AD.

The length of the segment KН = AB = 12 cm, since they are perpendicular to the blood pressure and BC. Then, by the Pythagorean theorem, MH ^ 2 = MK ^ 2 + KH ^ 2 = 25 + 144 = 169.

MH = 13 cm.

Since the MC is perpendicular to the AВСD, the plane of the MCВ is also perpendicular to the rectangle of the AВСD, and therefore the triangle of the ВМК is rectangular. Since point K is the middle of the sun, then ВС = 10/2 = 5 cm.

Then BM = 5 * √2 cm. The area of ​​the triangle ABM will be equal to: Sawm = AB * BM / 2 = 12 * 5 * √2 / 2 = 30 * √2 cm2.

The projection of the ABM triangle onto the rectangle is the ABK triangle, then Savk = AB * BK / 2 = 12 * 5/2 = 30 cm2.

The distance between straight lines ВM and AD is the side AB of the rectangle, since it is perpendicular to both straight lines. AB = 12 cm.

Answer: From point M to AD 13 cm. The area of ​​triangle ABM is 30 * √2 cm2. The area of ​​the AВK triangle is 30 cm2. Between straight ВM and AD 12 cm.



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.