Finding the area of ​​a square: formula and examples

Square is a geometric figure; regular quadrilateral, i.e. a quadrilateral having equal sides and angles (90°).

Area formula

1. By the length of the side: 

The area of ​​a square (S) is equal to the square of the length of its side:

S = a²

This formula follows from the fact that a square is a special case of a rectangle whose area is found by multiplying its adjacent sides:

S = a*b

And since all sides of a square are equal, then instead of a side b we again substitute the side into the formula aIe S = a*a = a².

2. Along the length of the diagonal

The area of ​​a square is half the square of the length of its diagonal:

S=d²/2

The ratio of the side and diagonal of the square: d=a√2.

Examples of tasks

Task 1

Find the area of ​​a square whose side is 7 cm.

Decision:

We use the formula for the length of the side, i.e. S=7² = 49 cm².

Task 2

Find the area of ​​a square whose diagonal is 4 cm.

1 Solution:

Let’s use the second formula (along the length of the diagonal): S = 4²/2 = 8 cm².

2 Solution:

We can express the length of the side in terms of the diagonal: a = 4/√2. And then, using the first formula, S = (4/√2)² = 8 cm².