Lateral Surface Area of Cube with Side Length Formula

Lateral Surface Area of Cube is the area of its four vertical faces, excluding the top and bottom faces. For a cube with side length a, the lateral surface area is 4a² square units. This page explains the formula, its derivation, related surface-area formulas, solved examples, and common cube problems for quantitative aptitude.

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What Is the Lateral Surface Area of a Cube?

The lateral surface area of a cube is the total area of its four side faces, excluding the top and bottom faces. If the side of the cube is a, its lateral surface area is 4a² square units.

Each face of a cube is a square with area a². The four vertical faces therefore have total area a² + a² + a² + a² = 4a². If the side is measured in centimetres, the answer is in square centimetres; if it is measured in metres, the answer is in square metres.

Lateral Surface Area of Cube Video Lessons

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Cube Volume, Surface Area and Diagonal

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Lateral Surface Area of Cube Formula & Tricks

Important Formulas

Lateral surface area
LSA = 4a²

Here, a is the side length of the cube. The formula adds the areas of four equal square faces.

Side from lateral surface area
a = √(LSA ÷ 4)

Use this formula when the lateral surface area is given and the side length is required.

Total surface area
TSA = 6a² = LSA + 2a²

A cube has six equal faces. Total surface area includes the four lateral faces and the top and bottom faces.

Lateral surface area using volume
LSA = 4∛(V²)

Since a = ∛V for volume V = a³, substituting into 4a² gives LSA = 4(∛V)².

Quick Tricks

Remember the four-face rule

For a cube, lateral surface area always means four equal side faces, so multiply the area of one face by 4.

Example: If a = 7 cm, one face is 49 cm² and LSA = 4 × 49 = 196 cm².
Use the ratio with total surface area

For the same cube, LSA : TSA = 4a² : 6a² = 2 : 3. Thus, LSA is two-thirds of TSA.

Example: If TSA = 150 cm², LSA = (2/3) × 150 = 100 cm².
Square the side before multiplying

Calculate a² first, then multiply by 4. This reduces errors in numerical calculations.

Example: For a = 12 m, 12² = 144, so LSA = 4 × 144 = 576 m².

Lateral Surface Area of Cube Concepts

Derivation from the Four Lateral Faces

A cube has four lateral faces, and each face is a square of area a²; therefore, its lateral surface area is 4a².

The front, back, left, and right faces are included. The top and bottom faces are excluded. Hence, LSA = a² + a² + a² + a² = 4a².

Example: For a cube of side 5 cm, LSA = 4 × 5² = 4 × 25 = 100 cm².

Finding Lateral Surface Area When the Side Is Given

Substitute the given side length into LSA = 4a² and express the result in square units.

The side must be squared because each lateral face is a square. If the side is converted from centimetres to metres, convert it before applying the formula when the answer is required in square metres.

Example: A cube has side 0.8 m. Its LSA = 4 × (0.8)² = 4 × 0.64 = 2.56 m².

Finding the Side from Lateral Surface Area

When LSA is known, divide it by 4 and take the square root: a = √(LSA ÷ 4).

This follows from LSA = 4a². The given area must be in square units, and the resulting side length is in the corresponding linear unit.

Example: If LSA = 324 cm², then a = √(324 ÷ 4) = √81 = 9 cm.

Lateral Surface Area Compared with Total Surface Area

The lateral surface area excludes two faces, while total surface area includes all six faces of the cube.

LSA = 4a² and TSA = 6a². Their ratio is LSA : TSA = 2 : 3. The difference between TSA and LSA is the area of the top and bottom faces, equal to 2a².

Example: For a = 6 cm, LSA = 144 cm² and TSA = 216 cm². Their difference is 72 cm², which equals 2 × 6².

Lateral Surface Area of Cube Visual Guide & Data

Use the table and chart below to understand the data better.

Surface Areas of a Cube

Comparison of lateral, top-and-bottom, and total surface areas for a cube of side a.

Surface portion Number of faces Area
Lateral faces 4 4a²
Top and bottom faces 2 2a²
All faces 6 6a²

Note: All areas are in square units when a is in linear units.

Four Faces Included in Cube Lateral Surface Area

Visual guide: Four Faces Included in Cube Lateral Surface Area
Side: a Lateral surface area: 4a²
The lateral surface area includes the four vertical faces and excludes the top and bottom faces.

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Practice Lateral Surface Area of Cube Questions

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1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Quick Revision Notes

Lateral Surface Area of Cube: Revision Points

Use these formulas and rules for quick revision.

  • Lateral surface area of a cube = 4a².
  • It includes four vertical faces and excludes the top and bottom faces.
  • Total surface area = 6a².
  • LSA : TSA = 2 : 3 for every cube.
  • Side from LSA = √(LSA ÷ 4).
  • The answer uses square units, such as cm² or m².
  • If the side is doubled, the lateral surface area becomes four times the original.
  • If the side is halved, the lateral surface area becomes one-fourth of the original.

Related Topic Explainers

Area of Square → Perimeter of Square → Area of Rectangle → Perimeter of Rectangle → Area of Triangle → Perimeter of Triangle → Heron's Formula → Area of Triangle Using Two Sides and Included Angle →

Lateral Surface Area of Cube FAQs

What is the lateral surface area of a cube with side 10 cm?

LSA = 4a² = 4 × 10² = 400 cm².

What is the lateral surface area of a cube with side 3.5 m?

LSA = 4 × (3.5)² = 4 × 12.25 = 49 m².

If the lateral surface area of a cube is 196 cm², what is its side?

a = √(196 ÷ 4) = √49 = 7 cm.

How is the lateral surface area different from the total surface area of a cube?

Lateral surface area includes four faces and equals 4a². Total surface area includes all six faces and equals 6a².

What happens to the lateral surface area when the side of a cube is doubled?

Since area varies as the square of the side, the new LSA is 4(2a)² = 4 times the original LSA.

A cube has a volume of 125 cm³. What is its lateral surface area?

Its side is ∛125 = 5 cm. Therefore, LSA = 4 × 5² = 100 cm².

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