Question

АВСД параллелограмм АД 12см, АВ 20см В 150 градусов. Найти площадь параллелограмма

Answer 1

Найдем угол A: Он равен 180 градусов-150 градусов=30 градусов

Теперь найдем площадь:

S=AB*AD*Sin угла A=12*20*(1/2)=120 см^2

Ответ: 120 см^2

Answer 2

Given Information

We are given the following information about the parallelogram ABCD: - AD = 12 cm - AB = 20 cm - ∠B = 150 degrees

Finding the Area of the Parallelogram

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

In a parallelogram, the base can be any of its sides. Since we are given the lengths of AD and AB, we can choose either of them as the base.

Let's choose AD as the base. To find the height, we need to determine the perpendicular distance between AD and BC.

To find the height, we can use trigonometry. Since we know the angle ∠B and the length of AB, we can use the sine function to find the height.

Let's calculate the height using the sine function: - sin(∠B) = height / AB - height = AB × sin(∠B)

Now, we can substitute the values into the formula to find the area: - Area = AD × height

Let's calculate the area of the parallelogram ABCD using the given information.

Calculation

- AB = 20 cm - ∠B = 150 degrees - AD = 12 cm

Using the sine function, we can calculate the height: - height = AB × sin(∠B) - height = 20 cm × sin(150 degrees) - height ≈ 20 cm × 0.5 - height ≈ 10 cm

Now, we can calculate the area using the formula: - Area = AD × height - Area = 12 cm × 10 cm - Area = 120 cm²

Answer

The area of the parallelogram ABCD is 120 cm².