what is the lateral surface area of a right hexagonal prism whose base is a regular hexagon with sides measuring 8 incheslong and altitude measuring 6 inches tall
lateral surface is perimeter*height. a hexagon's perimeter with a side of 8 inches= 48. to find the lateral area do 48*6.
To find the lateral surface area of a right hexagonal prism, follow these steps:
Step 1: Find the perimeter of the base.
Since the base is a regular hexagon with sides measuring 8 inches each, the perimeter of the base is equal to 6 times the length of one side.
Perimeter = 6 × 8 inches = 48 inches.
Step 2: Calculate the lateral surface area of one side of the prism.
The lateral surface area of the prism is equal to the perimeter of the base multiplied by the height of the prism. In this case, the height is given as 6 inches.
Lateral Surface Area of One Side = Perimeter × Height
Lateral Surface Area of One Side = 48 inches × 6 inches = 288 square inches.
Step 3: Determine the total lateral surface area of the hexagonal prism.
Since there are six identical sides on a hexagonal prism, you need to multiply the lateral surface area of one side by 6.
Total Lateral Surface Area = Lateral Surface Area of One Side × 6
Total Lateral Surface Area = 288 square inches × 6 = 1728 square inches.
Therefore, the lateral surface area of the right hexagonal prism is 1728 square inches.
To find the lateral surface area of a right hexagonal prism, we need to calculate the combined area of all the side faces excluding the top and bottom bases.
To start, let's find the area of one side face of the hexagonal prism. Each side face is in the shape of a rectangular trapezoid, with a longer base equal to the perimeter of the regular hexagon and a shorter base equal to the height of the prism.
The perimeter of a regular hexagon can be calculated by multiplying one side length by 6 (since a hexagon has six sides). In this case, the side length is given as 8 inches, so the perimeter of the hexagon is 8 * 6 = 48 inches.
Next, we need to find the height of the trapezoidal face. This height is equal to the altitude of the hexagonal prism, which is given as 6 inches.
Now we can calculate the area of one side face. The formula for the area of a trapezoid is given by (b1 + b2) * h / 2, where b1 and b2 are the lengths of the bases, and h is the height. In this case, b1 is the perimeter of the hexagon (48 inches) and b2 is the height of the prism (6 inches), so the area of one side face is (48 + 6) * 6 / 2 = 54 * 6 / 2 = 162 square inches.
Since the hexagonal prism has six identical side faces, the total lateral surface area can be found by multiplying the area of one side face by the number of side faces, which is 6: 162 * 6 = 972 square inches.
Therefore, the lateral surface area of the right hexagonal prism is 972 square inches.