Question

30 БАЛЛОВ Стороны параллелограмма равны 5 и 6, а угол между ними равен 150 градусам. Найдите площадь параллелограмма.

Answer 1

Ответ:   15 кв.ед.

Объяснение:

ABCD - параллелограмм. АВ=5 ВС=6.

Угол В=150*.

Проведем высоту ВН. Получили треугольник, у которого угол АВН=150*-90*=60*.  Тогда угол А=30*.

ВН - катет лежит против угла в 30*. Следовательно высота ВН=АВ* sin30*; или ВН=5*1/2=2,5.

Площадь  параллелограмма равна S=ah=6*2.5=15 кв.ед.

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 5 and 6, and the angle between them is 150 degrees. To find the height of the parallelogram, we can use trigonometry.

Let's break down the steps to find the area:

1. Find the height of the parallelogram using trigonometry. 2. Calculate the area using the formula.

Step 1: Finding the Height

To find the height of the parallelogram, we can use the formula:

height = side * sin(angle)

In this case, the side is 5 and the angle is 150 degrees. Let's calculate the height:

height = 5 * sin(150 degrees)

Using a calculator, we find that the sine of 150 degrees is 0.5. Therefore, the height is:

height = 5 * 0.5 = 2.5

Step 2: Calculating the Area

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

Area = base * height

In this case, the base is 6 and the height is 2.5. Let's calculate the area:

Area = 6 * 2.5 = 15

Therefore, the area of the parallelogram is 15 square units.

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