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Lateral surface area is finding the area of the sides of a three-dimensional geometric figure. The formulas for lateral surface area are based on the base of the figure and whether the figure is a prism, cone, or pyramid. We will investigate all of these.
Description of Lateral Surface Area
When a quarterback throws a sideways pass, he is throwing a lateral pass. The latissimus dorsi, or lats, is a muscle that runs along the sides and around to the back of the human body. Lateral indicates the side of something. Therefore, lateral surface area is found by finding the surface area of the sides of the object. This is done by finding the perimeter of the base and multiplying it by the height of any three-dimensional figure. Let’s look at some examples.
Lateral Surface of a Right Circular Cylinder
Let’s find the lateral surface of a right circular cylinder.
In this example, we are given a cylinder with a height of 6 cm and a diameter of 10 cm. Remember, in a right circular cylinder, the bases are circles. To find the lateral surface area, we find the perimeter, which in this case is the circumference (the distance around the circle), then multiply it by the height of the cylinder.
Right Circular Cylinder
The circumference of a circle is found using this formula:
Circumference of a Circle
The C stands for circumference, the d stands for the diameter, and the pi-symbol is rounded to 3.14. So we find the circumference of the base, 3.14 * 10 = 31.4, and then multiply this by the height, 6.
The reason we use circumference when finding lateral surface area is because when we open up the circular cylinder and lay the sides out flat, we end up with a rectangle. Think of a paper towel. A paper towel roll is a cylinder, but when you pull the paper towel off the roll, you end up with a rectangle. The length is the circumference and the width is the height of the roll.
lateral surface area cylinder
To find the area of the sides of this cylinder, we would multiply the circumference by the height. So, we have the formula for the lateral surface area of a right circular cylinder:
Lateral surface area of a right circular cylinder = circumference * height
LSA of Cylinder
Lateral Surface area formula for cylinder
LSA = 3.14 * 10*6
LSA = 188.4 cm
Lateral Surface Area of a Rectangular Prism
Let’s try another example, this time with a rectangular prism.
rectangular prism
As you can see the length, width, and height are given. So, the lateral surfaces are all the surfaces on the sides. We need to find the area of each of the four sides…. but there is a faster way—can you see it? If we found the perimeter of the base then multiplied it by the height, we would have the lateral surface area.
We have two lengths and two widths. As in the previous example, the basic formula for lateral surface area is:
Lateral Surface Area Formula
Just like the circular cylinder, if we laid the rectangular prism flat it would look like this:
Prism laid out flat
So, add up the lengths and widths and multiply by the height to find lateral surface area. We can write this more succinctly like this:
Lateral Surface Area Formula
Lateral Surface Area of a Rectangular Prism
 
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