Question

Соседние стороны параллелограмма равны 8см и 11см,а угол между ними равен 30.Найдите площадь параллелограмма. РЕШИТЬ НЕ ЧЕРЕЗ СИНУС И КОСИНУС!!!!!​​

Answer 1

Ответ:

44см²

Объяснение:

ABCD- параллелограм

АВ=8см

АD=11см

<А=30°

S(ABCD)=?

___________

Решение:

Проведем высоту ВН.

∆АВН- прямоугольный треугольник

ВН- катет против угла <А=30°

ВН=АВ/2=8/2=4см.

S(ABCD)=BH*AD=4*11=44см²

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 given information is that the adjacent sides of the parallelogram are 8 cm and 11 cm, and the angle between them is 30 degrees.

To find the height of the parallelogram, we can use trigonometry. However, you mentioned that you do not want to use sine or cosine. Therefore, we will use an alternative method.

Let's consider the given parallelogram:

     _______
    /       /
   /       /
  /_______/

The adjacent sides are 8 cm and 11 cm, and the angle between them is 30 degrees.

To find the height, we can draw a perpendicular line from one of the vertices to the opposite side, like this:

     _______
    /       /
   /   h   /
  /_______/

Let's call the height of the parallelogram 'h'.

Since the opposite sides of a parallelogram are parallel, the height 'h' is equal to the length of the perpendicular line we just drew.

Now, we have a right-angled triangle with one side of length 8 cm, the opposite side of length 'h', and the angle between them equal to 30 degrees.

We can use the properties of a 30-60-90 triangle to find the length of 'h'. In a 30-60-90 triangle, the ratio of the sides is 1:√3:2.

In our case, the side opposite the 30-degree angle is 'h', and the side adjacent to the 30-degree angle is 8 cm.

Using the ratio, we can find the length of 'h' as follows:

h = (8 cm) × (√3 / 2)

Simplifying this expression, we get:

h = 4√3 cm

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

Area = base × height
     = (11 cm) × (4√3 cm)
     = 44√3 cm²

Therefore, the area of the parallelogram is 44√3 cm².

Please note that the above solution assumes that the given angle is between the adjacent sides of the parallelogram. If the angle is between the non-adjacent sides, the solution will be different.