Lateral Surface Area of a Cube Formula with Examples

The lateral area of a cube formula represents the total surface area of all the side faces of the cube, excluding the top and bottom bases. To find this value, you calculate the area of the four vertical faces. Since a cube has six identical square faces, the formula is 4 multiplied by the side length squared, or LSA = 4a².

Understanding the Lateral Area of a Cube Formula and Surface Area

When we look at the math behind three-dimensional shapes like cubes, we usually focus on two different types of measurements: the total surface area and the lateral surface area. A cube is a perfect example of symmetry because every single one of its six faces is a square, and every square is exactly the same size. This makes using the surface area of a cube formula much easier than it might look at first.

The term "lateral" basically just means "side." So, the lateral surface area (LSA) is simply the area of the faces that aren't the top or the bottom. If you think about a box or a cube-shaped room, the lateral area is just the total space covered by the four walls. You ignore the floor and the ceiling. Since each wall is a square, and the area of a square is just the side length times itself (s²), the lateral area of a cube formula is:

LSA = 4s² (Where 's' stands for the side or edge length)

If you need to find the area of every single side, including the top and bottom, you would use the surface area of a cube formula for total area (TSA), which is:

TSA = 6s²

Knowing how these work is really helpful for real-world projects, like figuring out how much paint you need for the walls of a room without painting the floor. Whether you are doing the math manually or using a surface area of a cube formula calculator, the logic is always the same: find the length of one edge, square it, and then multiply by the number of faces you need to cover.

Exploring the Surface Area of a Cube Formula with Volume and Examples

Sometimes, math problems won't give you the side length directly. You might start with the volume instead. To solve these, you have to use the surface area of a cube formula with volume logic to work backward.

The volume (V) of a cube is found by cubing the side length (V = s³). So, to find the side length, you just take the cube root of the volume (s = ∛V). Once you have that number, you can jump right back into the area formulas.

Surface Area of a Cube Formula Example 1: The Basics

Let's say you have a cube where each side is 5 units long. To find the lateral surface area:

1. Start with the side length (s) = 5.

2. Apply the formula: LSA = 4s².

3. Calculation: LSA = 4 × (5 × 5).

4. LSA = 4 × 25.

5. LSA = 100 square units.

If you wanted the total surface area for that same cube:

1. Use the formula: TSA = 6s².

2. Calculation: TSA = 6 × (5 × 5).

3. TSA = 6 × 25.

4. TSA = 150 square units.

Surface Area of a Cube Formula Example 2: Working from Volume

Imagine you have a cube with a volume of 64 cubic units, and you need the lateral surface area.

1. First, find the side length: s = ∛64.

2. Since 4 × 4 × 4 = 64, your side length (s) is 4 units.

3. Now use the lateral area of a cube formula: LSA = 4s².

4. Calculation: LSA = 4 × (4 × 4).

5. LSA = 4 × 16.

6. LSA = 64 square units.

Helpful Things to Remember

• Square Units: Area is always written in square units (like cm², sq in, or m²) because it measures a flat surface.

• Perfect Squares: Every face of a cube is a perfect square (s²).

• The 4/6 Ratio: The lateral area is always exactly four-sixths (or two-thirds) of the total surface area.

Key Formulas for Cubes and Other Solids

While we are focusing on cubes, the concept of lateral area applies to cylinders, prisms, and other 3D shapes too. It always represents the "side" surfaces. Because a cube is a "regular" shape (everything is equal), the math is very consistent.

When you're working through these, just make sure all your measurements are in the same units. If your length is in inches, your area will be in square inches. If you happen to know the diagonal of the cube instead of the side, you can find the side length using geometry, but most of the time, you'll start with the edge length.

Make Mental Maths Easy and Confidence-Building with CuriousJr

Does your child feel unsure or get distracted while solving maths problems? Many children find maths confusing and stressful. With proper guidance and encouragement, maths can become simple, enjoyable, and confidence-building.

CuriousJr’s online mental maths classes are designed to make learning engaging and stress-free. These interactive sessions follow the school syllabus and focus on clear, practical explanations. Children improve speed, accuracy, and understanding while developing a positive interest in maths.