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SQUARE

DEFINITION

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

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

A drawing showing square with four right angles.

INTERESTING FACTS:

  • Because a square is a parallelogram like a rectangle or a rhombus, opposite sides are parallel and opposite angles are equal.
  • A square is a 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 RECTANGLE that has been "squeezed" so that all four (4) are equal.

TRADITIONAL FORMULA

AreaSquare = S2 or S x S or 4S

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

DEFINITION: TheSIDE (S) represents the length of any side of a square since they are all equal.

THINKING INSIDE THE BOX METHOD

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


KEY: Since a square can be thought of as a perfect rectangle, instead of having to learn another formula (AreaSquare = S2), treat S as both the width and height and simply use the rectangle formula (height x width) instead. See STEP-BY-STEP SOLUTION for detail example.

STEP-BY-STEP SOLUTION

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

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

AreaSquare = 4 in x 4 in = 16 in2

MEMORIZATION TIP

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