Finding the surface area of ​​a cube: formula and tasks

In this publication, we will consider how to find the surface area of ​​a cube and analyze examples of solving problems to fix the material.

The formula for calculating the area of ​​a cube

1. Through the length of the rib

The area (S) of the surface of a cube is equal to the product of the number 6 and the length of its edge squared.

S = 6 ⋅ a²

This formula is derived as follows:

• A cube is a regular geometric figure, all faces of which are equal squares with a side length a (it is also an edge of the cube).
• The area of ​​each face is calculated as follows: S = a ⋅ a = a².
• In total, a cube has 6 faces, which means that its surface area is equal to six areas of one face: S = 6 ⋅ a².

2. Through the length of the diagonal of the face

The side of any face of a cube (edge) can be calculated in terms of the length of its diagonal using the formula: a=d/√2.

This means that you can calculate the surface area of ​​uXNUMXbuXNUMXbthe figure as follows:

S = 6 ⋅ (d/√2)²

Examples of tasks

Task 1

Find the surface area of ​​a cube if its edge length is 12 cm.

Decision:

Using the first formula above, we get:

S = 6 ⋅ (12 cm)² = 864 cm².

Task 2

The surface area of ​​a cube is 294 cm². Calculate the length of its edge.

Decision:

Let’s take the edge of the cube as a. From the formula for calculating the area follows:

Task 3

Calculate the surface area of ​​a cube if the diagonal of its face is 5 cm.

Decision:

Let’s use the formula in which the length of the diagonal is involved:

S = 6 ⋅ (5 cm: √2)² = 75 cm².