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"?
390 x 15 = 5850 ?
you are correct if the "thickness" means the height of the material on the ground.
To find the lateral surface area of the "Z" shape, we need to calculate the surface area of the sides.
First, let's find the length of one side of the base of the "Z." We can do this by dividing the perimeter of the base by 4 since a "Z" shape has four equal sides.
Perimeter/4 = length of one side
390/4 = 97.5
Therefore, the length of one side of the base is 97.5 inches.
Now, let's calculate the area of one side of the "Z." Since we're dealing with a 3-dimensional shape, the surface area of one side can be found by multiplying the length of the side by the thickness of the "Z."
Area of one side = length of one side x thickness
Area of one side = 97.5 x 15
Area of one side = 1462.5 square inches
Since there are two sides in the "Z" shape, we need to multiply the area of one side by 2 to get the total lateral surface area.
Lateral surface area = 2 x Area of one side
Lateral surface area = 2 x 1462.5
Lateral surface area = 2925 square inches
Therefore, the lateral surface area of the "Z" is 2925 square inches.