Question

В параллелограмме две стороны равны 6 см и 8 см,а один из углов 150 градусов.найдите площадь парллелограмма?

Answer 1

в параллелограмме АВСД угол В=150*,уголА+уголВ=180*(как односторонние),значит угол А=30*.Из угла В опустить перпендикуляр на сторону АД.треугольник АВК прямоугольный,угол А=30*,тогда ВК=1/2АВ.АВ=6см,тогдаВК=3см.Площадь=ВК*АД=8*3=24см.кв

Answer 2

Calculation of the Area of a Parallelogram

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

In this case, we are given that two sides of the parallelogram are 6 cm and 8 cm, and one of the angles is 150 degrees.

To calculate the area, we need to find the height of the parallelogram. Since the height is perpendicular to the base, we can use trigonometry to find it.

Let's break down the solution step by step:

1. Find the height of the parallelogram using trigonometry: - We know that one of the angles of the parallelogram is 150 degrees. - The height of the parallelogram can be found using the formula: height = side × sin(angle). - Plugging in the values, we get: height = 6 cm × sin(150 degrees).

2. Calculate the area of the parallelogram: - Now that we have the height, we can calculate the area using the formula: Area = base × height. - Plugging in the values, we get: Area = 8 cm × (6 cm × sin(150 degrees)).

Let's calculate the area using these steps:

1. Find the height: - height = 6 cm × sin(150 degrees). - Using a calculator, we find that sin(150 degrees) = 0.5. - Therefore, height = 6 cm × 0.5 = 3 cm.

2. Calculate the area: - Area = 8 cm × (6 cm × sin(150 degrees)). - Plugging in the values, we get: Area = 8 cm × (6 cm × 0.5) = 8 cm × 3 cm = 24 cm².

Therefore, the area of the parallelogram is 24 cm².