Question

ABCD параллелограмм, BC=8,AB=6,угол BAH =30градусов, S=?Заранее спасибо)

Answer 1

Из вершины В проведем  высоту Н рассмотрим прямоугольный треугольник АВН  сторона ВН  равна 1/2 АВ так как находиться напротив угла в 30 градусов  ВН=3  А так как ВН -высота Параллелограмма то его площадь равна 8*3=24

Answer 2

Given Information

We are given the following information about the parallelogram ABCD: - BC = 8 - AB = 6 - Angle BAH = 30 degrees

We need to find the area of the parallelogram, denoted by S.

Solution

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

In a parallelogram, any side can be considered as the base. Let's consider AB as the base.

To find the height, we need to determine the perpendicular distance from side AB to side CD.

Since ABCD is a parallelogram, opposite sides are parallel. Therefore, the height is the perpendicular distance between AB and CD.

To find the height, we can use trigonometry. We know that angle BAH is 30 degrees, and we can use this angle to find the height.

Let's denote the height as h.

Using trigonometry, we can write: h = AB × sin(BAH).

Substituting the given values, we have: h = 6 × sin(30 degrees).

Now, we can calculate the value of h.

Calculation

Using the given values, we can calculate the height as follows:

h = 6 × sin(30 degrees)

Using a calculator, we find that sin(30 degrees) is equal to 0.5.

Substituting this value, we have:

h = 6 × 0.5 = 3

So, the height of the parallelogram is 3.

Now, we can calculate the area of the parallelogram using the formula: S = base × height.

Substituting the given values, we have:

S = AB × h = 6 × 3 = 18

Therefore, the area of the parallelogram ABCD is 18 square units.

Answer

The area of the parallelogram ABCD is 18 square units.