Math Antics: YouTube: Area:  https://youtu.be/xCdxURXMdFY
It is easier to see the "Square Units" when the figure is drawn on Graph Paper or the Coordinate Plane (X, Y) Graphing.
 
AREA is the SPACE inside of a 2-D or Flat Shape:
Parallelogram: (Rectangle, Square, Rhombus)
Triangles (Right, Isosceles, Equilateral, Scalene)
Circles
Other: Trapezoid, Kite

VOLUME is the SPACE inside of a 3-D Shape
Regular 3-D Shapes:  Cube, Prism (Rectangular Box or Triangular Tent), Sphere (ball), Cone, Pyramid, Cylinder

There are REGULAR shapes and IRREGULAR or COMPOUND/COMPLEX Shapes.
Complex Shapes can be broken down (Decomposed) into smaller regular shapes.

AREA: is measured in Units Squared or Square Units. (2 dimensions)
VOLUME is measured in Units Cubed or Cubed Units (3 dimensions)

IT IS IMPORTANT TO MAKE SURE ALL THE MEASUREMNTS IN A DIAGRAM ARE THE SAME UNITS. (Inches, Feet, Yards, Miles, Millimeters, Centimeters, Meters, Kilometers, etc.)

Area
Rectangle:  Area = Length x Width.  There a TWO Measures. Two Opposite sides are Equal and Parallel. Angles formed are 90 Degrees. 

Square:  Area = Length x Width.  There a TWO Measures. Opposite sides are Equal and Parallel. Angles formed are 90 Degrees. ALL SIDES ARE EQUAL:  So: AREA = Length x Length or Length^2.   This is where the SQUARE units comes from. The variable (S) is often used for the length of the measure of the SIDE:  Thus: AREA = Side^2

Parallelogram: Is like a Rectangle that has been pushed and is leaning. The Formula: Length x Width does not work anymore.  However, The Area = Base x Height.  Base is the Length of one side. HEIGHT is a word to describe the Perpendicular Distance from a Point to the Opposite Side.  In a Rectangle and Square, the Width does make a right angle; so, Width = Height.

Rhombus: A Rhombus is a Square that has been pushed and Leaning. The formula is still: Base x Height. A Rhombus is also a Parallelogram.  (It just has 4 equal sides).

Triangle:  Any Triangle can be "Duplicated", flipped and turned to make a Parallelogram.  Since a Parallelogram is Base x Height, but you have TWO triangles, Area = 1/2 x Base x Height or (Base x Height)/2.  

 

WORKSHEETS:
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End-Of-Page: Revised: April 17, 2024