Question

В параллелограмме MPOK диагональ PK перпендикулярна стороне MK.Найдите его площадь если сторона MP=10 см а сторона MK=8см.

Answer 1

Диагональ PK никак не может быть перпендикулярна MK

Answer 2

Calculation of the Area of a Parallelogram

To find the area of a parallelogram, we can use the formula: Area = base × height. In this case, the base of the parallelogram is the side MP, and the height is the perpendicular distance from side MP to side MK.

Given: - Side MP = 10 cm - Side MK = 8 cm

To find the height, we need to determine the length of the perpendicular PK from side MP to side MK. Since PK is perpendicular to MK, it forms a right angle with MK. Therefore, triangle MPK is a right triangle.

Using the Pythagorean theorem, we can find the length of PK. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, MP) is equal to the sum of the squares of the lengths of the other two sides (in this case, PK and MK).

Let's denote the length of PK as x. According to the given information, MP = 10 cm and MK = 8 cm. Applying the Pythagorean theorem, we have:

MP^2 = PK^2 + MK^2

Substituting the known values, we get:

10^2 = x^2 + 8^2

Simplifying the equation:

100 = x^2 + 64

Rearranging the equation:

x^2 = 100 - 64

x^2 = 36

Taking the square root of both sides:

x = √36

x = 6 cm

Therefore, the length of PK is 6 cm.

Now that we have the height (PK) and the base (MP), we can calculate the area of the parallelogram using the formula:

Area = base × height

Substituting the known values:

Area = 10 cm × 6 cm

Calculating the area:

Area = 60 cm^2

Therefore, the area of the parallelogram MPOK is 60 square centimeters.