Question

Начертите рисунок, запишите решение и ответ Стороны параллелограмма равны 6 см и 10 см и угол между ними 150 градусов. Найдите площадь параллелограмма.

Answer 1

Ответ:

Решение:

S = a·b·sin(α) = 6·10·sin(150°) = 60·sin(150°) ≈ 30 см²

Ответ: Площадь параллелограмма равна 30 см².

Answer 2

Problem Analysis

We are given a parallelogram with sides measuring 6 cm and 10 cm, and an angle of 150 degrees between them. We need to find the area of the parallelogram.

Solution

To find the area of a parallelogram, we can use the formula: Area = base * height.

In a parallelogram, the base is the length of one of the sides, and the height is the perpendicular distance between the base and the opposite side.

To find the height, we can use trigonometry. Since we know the angle between the sides, we can use the sine function to find the height.

Let's calculate the height first:

height = base * sin(angle)

Substituting the given values:

height = 6 cm * sin(150 degrees)

Now, let's calculate the area using the formula:

Area = base * height

Substituting the values:

Area = 6 cm * (6 cm * sin(150 degrees))

Now, let's calculate the area:

Area = 6 cm * (6 cm * sin(150 degrees))

Using a calculator, we find that the sine of 150 degrees is 0.5. Substituting this value:

Area = 6 cm * (6 cm * 0.5)

Area = 6 cm * 3 cm

Area = 18 cm^2

Therefore, the area of the parallelogram is 18 square centimeters.

Answer

The area of the parallelogram is 18 square centimeters.