Equilateral triangular prism surface area formula?

Answer 1

Ah, an equilateral triangular prism is a beautiful shape, isn't it? To find its surface area, you just need to add the areas of all its faces together. The formula is 3 times the base area (which is the area of one of the equilateral triangles) plus the lateral area (which is the perimeter of the base times the height). Just remember, there are no mistakes in math, only happy little accidents.

Answer 2

To find the surface area, the surface area of each rectangular side and the surface areas of the two triangular ends must be calculated. Given an equilateral triangular prism of height X and sides Y, each side has a surface area of X * Y. The end triangles are solved by using the Pythagorean theorem (a^2 + b^2 = c^2). In this case, a and c are known as Y and Y/2, so b= square root (Y^2 - (Y/2)^2). The area of a triangle is 1/2(base * height), where the base is Y and the height is b. The total surface area is then 3 * (X * Y) + 2 * ( 1/2 * (Y * (Y^2 - (Y/2)^2))).