The base of a prism is a regular hexagon that measures 4 cm on each side. The prism has a height of 13 cm. What is its total surface area?
To find the total surface area of a prism, we need to calculate the area of each face and then sum them all up.
Since the prism's base is a regular hexagon, we know that all of its six sides have equal length, which is 4 cm. To find the area of the hexagon, we need to use the formula:
Area = (3√3/2) × side length²
Plugging in the side length of 4 cm, we can calculate the area of the base.
Area of hexagon = (3√3/2) × 4 cm × 4 cm
Next, we need to calculate the area of the other five faces of the prism. Since they are all rectangles, we can find their areas using the formula:
Area = length × width
In this case, the length and width of each rectangle are the same as the side length of the hexagon, which is 4 cm.
Area of the other five faces = 5 × (side length × side length)
Once we have all six areas, we can sum them up to find the total surface area of the prism.
Total surface area = Area of hexagon + Area of the other five faces
Let's calculate:
Area of hexagon = (3√3/2) × 4 cm × 4 cm
Area of hexagon = 6√3 cm²
Area of the other five faces = 5 × (4 cm × 4 cm)
Area of the other five faces = 80 cm²
Total surface area = 6√3 cm² + 80 cm²
Finally, we can add the two areas together to find the total surface area of the prism.