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QUADRILATERAL

Quadrilateral > Parallelogram > Square

SQUARE

Definition

A square is a quadrilateral / parallelogram that has ALL FOUR (4) EQUAL SIDES with FOUR (4) RIGHT ANGLES (90°).

A right angle is an internal angle which is equal to 90°.

A drawing showing square with four right angles.

NOTES:

Because a square is a parallelogram like a rectangle or rhombus, opposite sides are parallel and opposite angles are equal.
A square is blend between a rectangle and a rhombus so it has the best of both worlds: A rectangle (four right angles) and a rhombus (four sides equal in length).

It Is Helpful To Think

It is helpful to think of a SQUARE as a perfect RECTANGLE because it has four (4) sides that are equal.

A drawing showing a square with four right angles.

Traditional Formula

Area_Square = S² or S x S

A drawing showing a square
with four sides of equal lenght
represent by the symbol S.

NOTE: S represents the length of any side of a square since they are all equal.

Thinking Inside The Box

If you place a SQUARE inside of a box (a square), you get a square. It's like placing a square peg in a square hole. Wow!!! Spell it backward: Wow

A drawing showing a square with numbers inside of them representing the number of square units in the square.

KEY: Since a square is a perfect box or a perfect rectangle, instead of having to learn another formula (Area_Square = S²), simply use the rectangle formula in its place.

Example

A square with a side of 4 in has an area of:

Treat any side (S) as both the height and the width since they are the same.
Use the rectangle formula instead (Area_Square = height x width).

Area_Square = 4 in x 4 in = 16 in²

REFERENCE: See screenshots above for graphic representations.

Memorization Tip

To help you remember the difference between a square and a rectangle, remember that a square has ALL four equal sides; whereas, a rectangle normally has two pairs of sides that are not equal.