Question

Стороны параллелограмма равна 10 см и 12 см. а один из углов равен 150 градусов . Найди площадь.

Answer 1

Дано: АВСД=парал-м; АВ=ДС=10см;ВС=АД=12см.Найти:площадь
1).Проведём высоту ВН
2.)Т.к.сумма углов парал-ма=360градусов, тогда, чтобы найти неизвестные углы(в парал-ме противоположные углы попарно равны) мы угол А=360:2-150=30 градусов.
3.)т.к. сторона, лежащая против угла 30 градусов равна половине гипотенузы, тогда ВН=10:2=5см
4.)площадь=АД*ВН=12*5=110см^2

Answer 2

Parallelogram Properties

To find the area of a parallelogram, we need to know the lengths of its sides and one of its angles. In this case, we are given that the sides of the parallelogram are 10 cm and 12 cm, and one of the angles is 150 degrees.

Calculating the Area

To calculate the area of a parallelogram, we can use the formula: Area = base × height. In a parallelogram, any side can be considered as the base, and the height is the perpendicular distance between the base and the opposite side.

In this case, we can choose the side with a length of 10 cm as the base. To find the height, we need to calculate the perpendicular distance between the base and the opposite side.

Finding the Height

Since we know the lengths of the sides and one of the angles, we can use trigonometry to find the height of the parallelogram. Let's consider the given angle of 150 degrees. Since the opposite angles in a parallelogram are equal, the opposite angle is also 150 degrees.

Using trigonometry, we can find the height using the formula: height = side × sin(angle).

Let's calculate the height using the given information:

height = 12 cm × sin(150 degrees)

To calculate the sine of 150 degrees, we can use a scientific calculator or an online calculator. The sine of 150 degrees is 0.5.

height = 12 cm × 0.5 = 6 cm

Calculating the Area

Now that we have the base (10 cm) and the height (6 cm), we can calculate the area of the parallelogram using the formula: Area = base × height.

Area = 10 cm × 6 cm = 60 cm²

Therefore, the area of the parallelogram is 60 square centimeters.

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