Question

Углы ромба относятся как 1:5, сторона 10 см. найти площадь ромба

Answer 1

Ответ: S=50см²

Объяснение: сумма односторонних углов ромба составляет 180°. Обозначим эти пропорции как х и 5х, составим уравнение:

5х+х=180

6х=180

х=180÷6

х=30°

Итак: угол1=30°, угол2=30×5=150°

Площадь ромба можно вычислить по формуле: S=а²×sinA=10²×sin30°=100×½=50

S=50см²

Answer 2

Finding the Area of a Rhombus

To find the area of a rhombus, we can use the formula: Area = (diagonal1 * diagonal2) / 2.

Given that the side of the rhombus is 10 cm, we can use the diagonals to find the area.

Diagonals of a Rhombus

The diagonals of a rhombus are perpendicular to each other and bisect each other at their point of intersection.

Calculating the Area

Using the formula for the area of a rhombus, we can calculate the area as follows:

Area = (diagonal1 * diagonal2) / 2

Let's assume the diagonals are represented by d1 and d2.

Given the side of the rhombus is 10 cm, we can use the Pythagorean theorem to find the length of the diagonals.

From the search results, we don't have direct information about the diagonals of the rhombus. Therefore, we'll calculate the diagonals using the side length.

Using the side length (10 cm), we can calculate the diagonals as follows:

d1 = 10 cm * sqrt(2) d2 = 10 cm * sqrt(2)

Now, we can calculate the area using the formula:

Area = (d1 * d2) / 2

Substituting the values: Area = (10 cm * sqrt(2)) * (10 cm * sqrt(2)) / 2 Area = (100 * 2) / 2 Area = 100 cm²

So, the area of the rhombus is 100 square centimeters.