Question

Очень прошу помощи. уделите пару минут с: сторона основания правильной четырехугольной призмы равна 4м, а диагональ боковой грани 5м. найти объем призмы

Answer 1

сторона основания с диагональю боковой грани и боковым ребром призмы образуют прямоугольный треугольник с катетом 4м (сторона основания), гипотенузой 5м (диагональ). Это египетский тр-к, поэтому второй катет (высота призмы) равен 3м.

Тогда Vпризмы=Sосн*h=4*4*3=48  

Answer 2

Объем призмы вычисляется как произведение площади основания на высоту

V = Sосн*h

В основании лежит квадрат со стороной а=4м, Sосн = а*а = 16 кв.м

Высоту определим по диагонали боковой грани h²=d²-a²=5²-4²=9, h=3м

V = a*a*h = 16*3 = 48 м³

 

Answer 3

Calculating the Volume of a Prism

To find the volume of a rectangular prism, we can use the formula:

Volume = Base Area × Height

In this case, the base area is the area of the rectangular base, and the height is the distance between the two bases.

Given Information

- The base of the prism has a length of 4 meters. - The diagonal of one of the lateral faces is 5 meters.

Calculating the Base Area

To calculate the base area, we can use the formula for the area of a rectangle:

Area = Length × Width

Since the base is a rectangle, we can use the given length and the width to calculate the base area.

Calculating the Width of the Base

The width of the base can be calculated using the Pythagorean theorem, as the diagonal and one side of the rectangle form a right-angled triangle.

Width = √(Diagonal^2 - Length^2)

Substituting the given values: Width = √(5^2 - 4^2) Width = √(25 - 16) Width = √9 Width = 3 meters

Calculating the Base Area

Now that we have the width, we can calculate the base area: Base Area = Length × Width Base Area = 4 meters × 3 meters Base Area = 12 square meters

Calculating the Volume

Now that we have the base area and the height, we can calculate the volume of the prism using the formula: Volume = Base Area × Height

Substituting the given values: Volume = 12 square meters × Height

Unfortunately, the search results did not provide the height of the prism. If you have the height of the prism, please provide it so that I can calculate the volume for you.