Question

Найдите площадь параллелограмма со сторонами 12 и 14 и углом 150°​

Answer 1

Ответ:

S= 12*14=168 см^2

Объяснение:

вроде так

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 12, and the height can be determined using trigonometry.

Calculating the Height of the Parallelogram

To calculate the height of the parallelogram, we can use the given angle of 150° and the side lengths of 12 and 14. We can use the Law of Cosines to find the height.

The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab cos(C)

In this case, we can consider the side lengths of the parallelogram as the two sides of a triangle, and the angle between them as the angle C. Let's calculate the height using this formula.

Using the given side lengths of 12 and 14, and the angle of 150°, we can substitute these values into the Law of Cosines equation:

c^2 = 12^2 + 14^2 - 2(12)(14)cos(150°)

Simplifying the equation:

c^2 = 144 + 196 - 336cos(150°)

c^2 = 340 - 336cos(150°)

Now, we can calculate the value of c^2:

c^2 = 340 - 336(-0.866)

c^2 = 340 + 291.776

c^2 = 631.776

Taking the square root of both sides:

c ≈ 25.14

Therefore, the height of the parallelogram is approximately 25.14.

Calculating the Area of the Parallelogram

Now that we have the base (12) and the height (25.14), we can calculate the area of the parallelogram using the formula:

Area = base × height

Area = 12 × 25.14

Area ≈ 301.68

Therefore, the area of the parallelogram with side lengths 12 and 14 and an angle of 150° is approximately 301.68 square units.

Please note that the calculations provided are based on the given information and may vary slightly depending on the rounding of decimal places.

Let me know if there's anything else I can help you with!