Base Area: 22 square inches
Lateral Surface Area: 308 square inches
What is the Surface Area of the hexagonal prism?
As=2*Ab + Al = 2*22 + 308 = 352 Sq. In.
SORRY! The calculated surface area was for a rectangular prism NOT a hexagonal
prism.
As = 2*22 + 308 = 352 Sq. In.
Same as previous results.
To find the surface area of a hexagonal prism, you need to find the sum of the areas of all its faces.
The hexagonal prism has three pairs of congruent rectangular faces. Each pair consists of the top and the bottom face, which are congruent hexagons, and the four rectangular faces around the sides.
To find the area of the top and bottom hexagons, you can use the formula:
Area = (3√3/2) * s^2
where s represents the side length of the hexagon.
Since the area of the base is given as 22 square inches, we can solve for s:
22 = (3√3/2) * s^2
To find the area of the rectangular faces, you need to determine the dimensions of each rectangle. You can do this by dividing the given lateral surface area by the perimeter of the hexagon. Since the hexagon has six equilateral sides, you can use the formula:
Perimeter = 6s
Now, let's calculate the side length of the hexagon:
Perimeter = 6s
308 = 6s
Divide both sides of the equation by 6 to find the side length s of the hexagon:
s = 308/6 = 51.33 inches (rounded to two decimal places)
Next, substitute the calculated value for s into the formula for the area of a hexagon to find the areas of the top and bottom hexagonal faces.
Area = (3√3/2) * s^2
Area = (3√3/2) * (51.33)^2
Calculate the area of the hexagons using this formula.
Next, calculate the area of the rectangular faces. Since there are four of these faces, you can multiply the area of one by 4.
Finally, add the areas of all the faces (top, bottom, and rectangular) to find the surface area of the hexagonal prism.