Question

The volume of the regular triangular prisms is v. What must be the side of prism to be a total surface area of prism minimum?​

Answer 1

Answer:

Step-by-step explanation:

The volume of a triangular prism is equal to the product of the triangular base area and the height of the prism.

Volume = Area of the Base × Height of prism

Volume of Triangular Prism = ½ × b × h × l

Where b is the base length, h is the height of the triangle and l is the length between the triangular bases.

Surface area of triangular prism is equal to the sum of the lateral surface area and twice the base area of the triangular prism. It is measured in square units.

Surface area of triangular prism = 2A + PH

Where A is the area of the triangular bases, P is the perimeter of the bases and H is the height of the prism.

Now, Area of the base= ½ × b × h

If suppose, a, b and c are the sides of the triangular bases, then,

Perimeter of the base = a + b + c

Therefore,

Surface area of triangular prism = 2(½ × b × h) + ( a + b + c)H

Area of the Triangular Prism = (bh + ( a + b + c)H)

Where b and h is the base and height of the bases, respectively and H is the height of the prism.