The Z company specializes in caring for zebras. They want to make a 3-dimensional "Z" to put in front of their company headquarters. The "Z" is 15 inches thick and the perimeter of the base is 390 inches. What is the lateral surface area of this "Z"?
10.4
2T3ty
To find the lateral surface area of the 3-dimensional "Z," we need to calculate the area of all the sides excluding the top and bottom surfaces.
Step 1: Calculate the base perimeter:
Given that the perimeter of the base is 390 inches, we can divide this by 4 (as "Z" has four corners) to find the length of each side of the base:
390 inches / 4 = 97.5 inches
Step 2: Calculate the area of each side:
The lateral surface area of a prism (which includes a rectangular shape like the "Z") can be calculated by multiplying the perimeter of the base by the height of the prism.
Since the "Z" is 15 inches thick, the height of each side is 15 inches.
So, the area of each side of the "Z" is:
97.5 inches (perimeter of the base) × 15 inches (height of each side) = 1462.5 square inches
Step 3: Calculate the total lateral surface area of the "Z":
Since the "Z" has four sides, we need to multiply the area of each side by 4:
1462.5 square inches (area of each side) × 4 = 5850 square inches
Therefore, the lateral surface area of the 3-dimensional "Z" is 5850 square inches.
To find the lateral surface area of the "Z," we need to calculate the area of the four sides that make up the thickness of the "Z."
First, let's start by finding the dimensions of the base of the "Z." Since the perimeter of the base is given as 390 inches, we can divide that by 4 to find the length of each side.
390 inches ÷ 4 = 97.5 inches
Therefore, each side of the base of the "Z" measures 97.5 inches.
Now, let's calculate the lateral surface area. Since all sides of the "Z" are identical rectangles, we only need to find the area of one side and then multiply it by four.
The area of a rectangle is given by the formula: A = length x width.
The length of each side is the height of the "Z," which is 15 inches. The width is the perimeter of the base divided by 4, which we found to be 97.5 inches.
So, the area of one side is: A = 15 inches x 97.5 inches = 1462.5 square inches.
Since there are four identical sides, we multiply the area of one side by four:
Lateral Surface Area = 4 x 1462.5 square inches = 5850 square inches.
Therefore, the lateral surface area of the "Z" is 5850 square inches.