Top Area: 26 square inches

Top Perimeter: 34 inches
Height: 11 inches

What is the Surface Area of the 12-sided prism?

what is top perimeter*height? Answer: side surface area

then add that to top, bottom area

To find the surface area of a 12-sided prism, you need to calculate the sum of the areas of all its sides. Let's break it down step by step.

First, divide the prism into two parts: the top and the rectangular sides.

The top of the prism is a regular polygon with 12 sides. Since you know the top perimeter is 34 inches, you can divide it by 12 to find the length of one side. Thus, each side measures 34/12 = 2.8333... inches.

The formula to calculate the area of a regular polygon is: Area = (perimeter * apothem) / 2.

To find the apothem (the distance from the center of the polygon to the midpoint of one of its sides), you can divide the side length by 2 times the tangent of half the central angle. Since it's a regular polygon, the central angle equals 360 degrees divided by the number of sides (12 in this case). Therefore, the apothem is (2.8333... / (2 * tan (360/12/2))) inches.

Now you can calculate the area of the top polygon by plugging in the values into the formula: Area = (34 * apothem) / 2.

Next, calculate the area of the rectangular sides. The height of the prism is given as 11 inches, so each side of the rectangle has a length of 11 inches. The perimeter of each side is equal to the top perimeter since they are the same size.

Since there are 12 sides, multiply the height by 12 to get the total area of the rectangular sides.

Finally, add the area of the top and the area of the rectangular sides to get the total surface area of the prism.

So, using the above calculations, you can find the surface area of the 12-sided prism.