Question

Помогите ребят сторона параллелограмма равна 10 см. , а диагональ, равная 12см образует с ней угол 30 градусов. найдите площадь параллелограмма

Answer 1

Диагональ делит параллелограмм на 2 равных треугольника. следовательно, нужно найти площадь одного из них: 

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 base of the parallelogram is given as 10 cm. However, we need to find the height of the parallelogram.

Finding the Height of the Parallelogram

To find the height of the parallelogram, we can use the given information that one of the diagonals forms a 30-degree angle with the side of the parallelogram.

Let's denote the diagonal as d and the height as h. We can use trigonometry to find the height.

In a parallelogram, the diagonals bisect each other, so we can divide the diagonal d into two equal parts. Each part will be d/2.

We can consider one of the right triangles formed by the diagonal and the height. The angle between the diagonal and the base is 30 degrees.

Using trigonometry, we can write:

tan(30 degrees) = h / (d/2)

Simplifying this equation, we get:

h = (d/2) × tan(30 degrees)

Now, we can substitute the given values into this equation to find the height.

Calculating the Height

The given diagonal is 12 cm, and it forms a 30-degree angle with the side of the parallelogram.

Substituting these values into the equation, we get:

h = (12/2) × tan(30 degrees)

Calculating this expression, we find:

h ≈ 3.464 cm

Calculating the Area

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

Area = base × height

Substituting the values, we get:

Area = 10 cm × 3.464 cm

Calculating this expression, we find:

Area ≈ 34.64 cm²

Therefore, the approximate area of the parallelogram is 34.64 square centimeters.

Please note that the calculations provided are based on the given information and assumptions made.