Question

Стороны параллелограмма равны 4см и 6см один угол 60 градусов.Найти Sпар-?

Answer 1

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Answer 2

Given Information

We are given that the sides of the parallelogram are equal to 4 cm and 6 cm, and one angle measures 60 degrees.

Solution

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

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

Since we are not given the height directly, we need to find it using the given information.

Let's consider the given parallelogram:

     A _______ B
      /       \
     /         \
    /           \
   /_____________\
  D               C

We know that AB = 4 cm and BC = 6 cm. We are also given that angle ABC measures 60 degrees.

To find the height, we can use trigonometry. We can consider triangle ABC and use the sine function to find the height.

The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In triangle ABC, the side opposite angle ABC is the height (h), and the hypotenuse is AB.

Using the sine function, we have:

sin(60 degrees) = h / AB

Simplifying, we get:

h = AB × sin(60 degrees)

Now, we can substitute the values:

h = 4 cm × sin(60 degrees)

Using a calculator, we find that sin(60 degrees) is equal to √3/2.

Substituting this value, we have:

h = 4 cm × (√3/2)

Simplifying further, we get:

h = 2√3 cm

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

Area = base × height

Substituting the values, we have:

Area = 4 cm × 2√3 cm

Simplifying, we get:

Area = 8√3 cm²

Therefore, the area of the parallelogram is 8√3 cm².

Answer

The area of the parallelogram is 8√3 cm².