In a regular triangular prism, the side of the base is 3 cm and the height of the prism is 8 cm.

In a regular triangular prism, the side of the base is 3 cm and the height of the prism is 8 cm. Calculate the total surface area of the prism.

In a regular triangular prism, it is known:

Base side = 3 cm;
The height of the prism is 8 cm.
Let’s calculate the total surface area of the prism.

1) First, we find the area of the base.

Since all sides are equal, then the area is found by the formula:

S = a ^ 2/4 * √3 = 3 ^ 2/4 * √3 = 9/4√3 cm ^ 2;

2) Find the area of the lateral surface.

S = P * h;

P = a + a + a = 3 * a = 3 * 3 = 9 cm;

Then:

S = 9 cm * 8 cm = 9 * 8 cm ^ 2 = 72 cm ^ 2;

3) Now we find the total area of the prism:

S = Side + 2 * Sb = 72 cm ^ 2 + 2 * 9 / 4√3 cm ^ 2 = (72 + 4.5√3) cm ^ 2 = 79.65 cm ^ 2 = 80 cm ^ 2.