Question

В равнобедренной трапеции меньшее основание равно 4 см, боковая сторона 6 см, а один из углов равен 120 градусов. Найти площадь трапеции ( помогите пожалуйста)

Answer 1

трапеция АВСД, 

высота ВН

угол Б=120

решение - 

1) угол АВН = 120-90=30

АН = 6/2= 3

следовательно 

2) АД= 4+3+3 = 10

3) высота ВН по т. Пифа = 3корень-из-3

4) средняя линия = 4+10 /2 = 7

5) площадь = 3корень-из-3 * 7 = 21корень-из-3

Answer 2

Calculation of the Trapezoid's Area

To find the area of a trapezoid, we can use the formula:

Area = (a + b) * h / 2

where: - a and b are the lengths of the bases of the trapezoid, - h is the height of the trapezoid.

In this case, we are given that the smaller base of the trapezoid is 4 cm, the side length is 6 cm, and one of the angles is 120 degrees.

Let's calculate the area step by step:

1. First, we need to find the length of the larger base. To do this, we can use the given side length and the angle.

From the given information, we know that one of the angles is 120 degrees and the side length is 6 cm. However, we don't have enough information to directly calculate the larger base.

2. Next, we can use the Law of Cosines to find the length of the larger base. 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 trapezoid as a triangle by extending the smaller base to form a right triangle. The larger base will be the hypotenuse of this right triangle.

Let's denote the larger base as c, the smaller base as a, and the side length as b. The angle opposite side c is 120 degrees.

Plugging in the values into the Law of Cosines equation, we get:

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

c^2 = 4^2 + 6^2 - 2 * 4 * 6 * cos(120°)

Solving this equation will give us the length of the larger base.

3. Once we have the lengths of both bases, we can calculate the height of the trapezoid. The height is the perpendicular distance between the bases.

4. Finally, we can substitute the values of the bases and the height into the formula for the area of a trapezoid to find the answer.

Please note that without the exact values of the larger base and the height, we cannot provide the precise calculation for the area of the trapezoid. However, you can follow the steps outlined above to calculate it yourself using the given information.

Let me know if you need any further assistance!