Question

Основанием наклонной призмы является параллелограмм, стороны которого равны 6 дм и 7 дм, а один из углов 45 градусов. Боковое ребро призмы равно 8 дм и наклонено к плоскости основания под углом 45 градусов. Вычислить объем призмы С полным объяснением, если можно, пожалуйста))

Answer 1

Sabcd=bh*ad
sin 45=bh/ab
√2/2=bh/6
bh=√2*6/2=3√2 дм^2
sin 45=a1h1/aa1
√2/2=a1h1/8
a1h1=8√2/2=4√2
Sabcd=3√2*7=21√2
V=Sabcd*а1h1=4√2*21√2=168 дм^3

Answer 2

Calculation of the Volume of a Prism

To calculate the volume of a prism, we need to know the area of the base and the height of the prism. In this case, the prism is inclined, and its base is a parallelogram with sides measuring 6 dm and 7 dm, and one of the angles measuring 45 degrees. The lateral edge of the prism is 8 dm and is inclined to the base plane at an angle of 45 degrees.

To find the volume of the prism, we can follow these steps:

Step 1: Calculate the area of the base of the prism. Since the base is a parallelogram, we can use the formula for the area of a parallelogram: Area = base * height. In this case, the base is 6 dm and the height can be calculated using trigonometry. Since one of the angles of the parallelogram is 45 degrees, we can use the sine function to find the height. The height can be calculated as height = base * sin(angle).

Using the given values, we can calculate the height of the base as follows: height = 6 dm * sin(45 degrees) = 6 dm * 0.7071 ≈ 4.2426 dm.

Therefore, the area of the base of the prism is: Area = 6 dm * 4.2426 dm ≈ 25.4556 dm².

Step 2: Calculate the volume of the prism. The volume of a prism is given by the formula: Volume = base area * height. In this case, the base area is 25.4556 dm² (calculated in Step 1) and the height is the length of the lateral edge, which is 8 dm.

Using the given values, we can calculate the volume of the prism as follows: Volume = 25.4556 dm² * 8 dm = 203.6448 dm³.

Therefore, the volume of the prism is approximately 203.6448 cubic decimeters (dm³).

Please note that the calculations provided are based on the information given in the question. If there are any additional details or assumptions, please let me know, and I'll be happy to assist you further.