An equilateral triangular prism is pictured. The height of the base is 3.46 cm

what is the surface area of the prism?

1 answer

To calculate the surface area of an equilateral triangular prism, we need to find the areas of the two triangular bases and the three rectangular faces.

First, let's find the area of the triangular bases. Since the triangle is equilateral, all sides are equal.

The area of an equilateral triangle can be calculated using the formula:
Area = (sqrt(3) / 4) * side^2

In this case, the side of the equilateral triangle is the height of the base, which is 3.46 cm.

Area of one triangular base = (sqrt(3) / 4) * 3.46^2 = 5.98 cm^2

Since there are two triangular bases, the total area of the triangular bases is:
Total base area = 2 * 5.98 = 11.96 cm^2

Next, let's find the area of the three rectangular faces. Each face is a rectangle with one side equal to the height of the base (3.46 cm) and the other side equal to the length of the prism (also 3.46 cm since it is an equilateral prism).

Area of one rectangular face = 3.46 * 3.46 = 11.92 cm^2

Since there are three rectangular faces, the total area of the rectangular faces is:
Total rectangular face area = 3 * 11.92 = 35.76 cm^2

Finally, to find the total surface area of the prism, we add the area of the triangular bases to the area of the rectangular faces:
Total surface area = Total base area + Total rectangular face area
Total surface area = 11.96 + 35.76 = 47.72 cm^2

Therefore, the surface area of the equilateral triangular prism is 47.72 cm^2.