About Lateral Surface Area of a Cube
A cube's lateral surface area is equal to the total area of the cube's side faces. A cube is a three-dimensional object with six congruent square faces. The cube's six square faces are all the same size. A cube is also known as:
A normal hexahedron (since it has six congruent faces) and a square prism (as its top and bottom faces are squares)
A cube is 1 of the five platonic solids to be noticed. A Rubik's cube, a dice (with square faces), an ice cube, and other real-life cubes are examples. Let's look at what the lateral surface area of a cube is, as well as the formula, a few examples, and some practice questions.
The formula for Lateral Surface Area (L.S.A) of a Cube
'Lateral' refers to something that is on the side. As a result, a cube's lateral surface area is equal to the sum of its side faces. Can you figure out how many sides a cube has? Yes, there are four sides (because there are 6 faces in total, among which if we remove the top and the bottom faces, there are only 4 side faces). The lateral area of a cube is equal to sum of its four side faces. A cube's lateral area is also known as its lateral surface area (LSA). The area of the lateral surface is measured in square units.
Consider a cube of edge length 'x'. Each of its faces is a square, the area of each face = x2 square units.
The lateral surface area (LSA) of cube = sum of areas of all four side faces ⇒ LSA of the cube = x2 + x2 + x2 + x2 = 4x2
L.S.A = 4x2
Lateral Surface Area (L.S.A) of Cube with Diagonal
We need to remember the link between the edge length (x) and the space diagonal (d) of a cube in order to compute the lateral area of a cube when the space diagonal is given. The relationship between a cube's side length (x) and its space diagonal (d) is given by
d = x √3 ⇒ x = d / √3
Substituting this in the formula of the lateral surface area of a cube,
L.S.A = 4x2
= 4 (d / √3)2
= 4d2 / 3
Thus, the LSA of the cube when its diagonal (d) is given = 4d2 / 3. The lateral area of a cube of the edge length 'x' is 4x2 & the lateral area of a cube of space diagonal 'd' is 4d2/ 3.
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