Question

Стороны основания прямой треугольной призмы 6дм, 10дм и 14дм. Площадь боковой поверхности 300(дм в квадрте ) найти обьем призмы )

Answer 1

  V=S*H

S=2*Sосн.+Sбок.

 Sбок.=P*H, H= Sбок. /H =300/15=20 дм

 P=1/2(6+14+10)=15 дм

 Sосн.=корень квадратный из p*(p-a)*(p-b)*(p-c)=25,98 дм

 S=2*25,98+300=351,96  дм2

 V= 351,96*20=7039,2  дм3 

 

 

 

 

 

 

 

 

 

 

Answer 2

Sides of the Right Triangular Prism

To find the volume of a right triangular prism, we need to know the lengths of its sides. In this case, the given lengths are 6 dm, 10 dm, and 14 dm.

Surface Area of the Lateral Faces

The surface area of the lateral faces of a prism can be calculated by finding the sum of the areas of each face. In this case, the given surface area is 300 dm².

Calculating the Volume

To find the volume of a prism, we multiply the area of the base by the height. Since the base of the prism is a right triangle, we can use the formula for the area of a right triangle: Area = (1/2) * base * height.

In this case, the base of the prism is the right triangle with sides 6 dm and 10 dm. The height of the prism is 14 dm.

Let's calculate the volume:

Volume = Area of the base * Height

Volume = (1/2) * 6 dm * 10 dm * 14 dm

Volume = 420 dm³

Therefore, the volume of the given prism is 420 cubic decimeters (dm³).

Please let me know if there is anything else I can help you with!