# Square

## Definition

It is a geometric shape having four equal line segments that intersect at four points to create four internal angles of 90° each.

## Properties

1. All four interior angles are right angles; in □ ABCD, ∠ABC = ∠BCD = ∠CDA =∠DAB =  90°
2. Has four vertices and four sides; A, B, C and D are vertices and AB, BC, CD and DA are sides
3. All four sides are congruent; so AB ≅ BC ≅ CD ≅DA
4. Opposite sides are parallel to each other; AB ∥ CD and BC ∥ DA
5. Diagonals of the square bisect each other at 90°
6. Two diagonals of the square are perpendicular to each other; AC = BD

## Formulas

### Diagonal

The segment that connects two opposite vertices of the square at right-angle to each other. The formula is given below:

Diagonal (d) = a × √2, here a = side length

Problem: Finding the diagonal of a square when only the SIDES are known

Find the diagonal of a square whose sides measure 4 cm.

Solution:

As we know,
Diagonal (d) = a × √2, where a = 4 cm
= 4 x √2 cm
= 5.656 cm

### Area

The total space enclosed by the square. The formula is given below:

Area (A) = a2, here a = side length

Problem: Finding the area of a square when only the SIDES are known

Find the area of a square whose sides measure 6 cm.

Solution:

As we know,
Area (A) = a2, where a = 6 cm
= 6 x 6 cm2
= 36 cm2

### Perimeter

The total distance covered around the edge of the square. The formula is given below:

Perimeter (P ) = 4a ,here a = side length

Problem: Finding the perimeter of a square when only the SIDES are known

Find the perimeter of a square whose sides measure 10 cm.

Solution:

As we know,
Perimeter (P ) = 4a,where a = 10 cm
= 4 x 10 cm
= 40 cm

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