Question

Найдите объем правильной треугольной призмы, если сторонаа её основания равна 6 дм, а боковое ребро 7 дм. *Ответ:63 корень из 3 дм в кубе. Напишите решение пожалуйста.

Answer 1

V=Sосн * h

 

Socн=\/p*(p-a)*(p-b)*(p-c), где p-это полупериметр треугольника, а, b,c соответственно стороны треугольника. Т.к. это правильный треугольник, то все его стороны будут по 6 см. 

Полупериметр находим по формуле: р=Р/2

р=(6+6+6)/2=9см

 

Sосн=\/9*(9-6)(9-6)(9-6)=\/9*3*3*3=9\/3 cм^2

 

Боковое ребро в призме, это та же самая высота, значит h=7

 

V=9\/3*7=63\/3см^3

 

Ответ: 63\/3см^3

 

Если, что-то не понятно, пиши =)

Answer 2

Calculation of the Volume of a Right Triangular Prism

To find the volume of a right triangular prism, we need to know the length of the base, the height of the prism, and the length of one of the lateral edges. In this case, we are given that the length of the base is 6 dm and the length of the lateral edge is 7 dm.

The formula to calculate the volume of a right triangular prism is:

Volume = (1/2) * base * height * lateral edge

Let's substitute the given values into the formula:

Volume = (1/2) * 6 dm * height * 7 dm

To find the height, we need to use the Pythagorean theorem, as the prism is right triangular. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the base of the triangle is 6 dm, and the lateral edge is 7 dm. Let's denote the height as 'h'. Using the Pythagorean theorem, we can write the equation:

6^2 + h^2 = 7^2

Simplifying the equation:

36 + h^2 = 49

h^2 = 49 - 36

h^2 = 13

Taking the square root of both sides:

h = √13 dm

Now we can substitute the value of the height into the volume formula:

Volume = (1/2) * 6 dm * √13 dm * 7 dm

Simplifying the expression:

Volume = 63√3 dm^3

Therefore, the volume of the right triangular prism is 63√3 dm^3.

Solution:

The volume of the right triangular prism with a base side length of 6 dm and a lateral edge length of 7 dm is 63√3 dm^3.