Question

В параллелограмме из вершины тупого угла проведены высоты, равные 6 см и 8 см . Найдите площадь параллелограмма, если угол между высотами равен 60 градусов Решите пожалуйста , подробно

Answer 1

Решение......................

Answer 2

Finding the Area of a Parallelogram

To find the area of a parallelogram when the lengths of the two heights and the angle between them are given, we can use the formula:

Area = base * height

However, in this case, we need to find the base of the parallelogram using the given heights and the angle between them.

Calculating the Base of the Parallelogram

To find the base of the parallelogram, we can use the formula:

base = (height1 + height2) / tan(angle)

Given: - Height 1 = 6 cm - Height 2 = 8 cm - Angle between the heights = 60 degrees

Using the given values, we can calculate the base of the parallelogram:

base = (6 + 8) / tan(60)

base = 14 / tan(60)

base ≈ 14 / 1.732

base ≈ 8.09 cm

Calculating the Area of the Parallelogram

Now that we have found the base of the parallelogram, we can use the formula to calculate the area:

Area = base * height

Area = 8.09 * 6

Area ≈ 48.54 cm²

Therefore, the area of the parallelogram is approximately 48.54 square centimeters.