Question

Стороны параллелограмма равны 24 дм и 18 дм. Найдите его площадь, если известно, что угол между сторонами равен 60°

Answer 1

Площадь параллелограмма: S=ab·sinα=24·18·√3/2=216√3 дм² - это ответ.

Answer 2

Finding the Area of a Parallelogram

To find the area of a parallelogram, we can use the formula:

Area = base × height

In this case, the sides of the parallelogram are given as 24 dm and 18 dm, and the angle between the sides is 60°. We need to find the height of the parallelogram in order to calculate its area.

To find the height, we can use trigonometry. The height of the parallelogram is the perpendicular distance between the two parallel sides. Since we know the length of one side (24 dm) and the angle between the sides (60°), we can use the sine function to find the height.

The formula for the height of a parallelogram is:

height = side × sin(angle)

Let's calculate the height using this formula:

height = 24 dm × sin(60°)

To calculate the sine of 60°, we can use a calculator or refer to a trigonometric table. The sine of 60° is √3/2.

height = 24 dm × √3/2

Now, let's substitute the values into the formula to find the height:

height = 24 dm × √3/2

height ≈ 20.7846 dm

Now that we have the height, we can calculate the area of the parallelogram using the formula:

Area = base × height

Area = 18 dm × 20.7846 dm

Area ≈ 374.1232 dm²

Therefore, the area of the parallelogram is approximately 374.1232 square decimeters.

Please note that the calculations are approximate due to rounding.