1. A. Definition
Square have different meanings in mathematic, but they all point to the same
basic mathematical concept. Square have the same meaning with quadratic. The
term quadratic describes something that pertains to squares, to the operation of
squaring, to terms of the second degree, or equations or formulas that involve
such terms. Quadratus is Latin for square.
When you square something, it is multiplied by itself. For example, 3
squared means 3 × 3. An equation where the highest exponent of the variable
(usually "x") is a square (2). So it will have something like 𝑥2
, but not 𝑥3
etc.
This common operation is notated with an exponent of 2. Using this notation,
3×3 is indicated with 32
and is read as '3 squared' or '3 to the second power' or
'3 to the power of 2'. Squaring is not just limited to numbers, however. You can
square variables or even complex mathematical expressions.
Whenever a quantity is squared, the result will always be positive. If you
square a number, the answer is always positive because (-)×(-) = (+). For
example, 32
= 3×3= 9 and (-3)2 = (-3)×(-3) = 9.
Square also has a specific meaning in geometry. A Square is a flat shape with 4
equal sides and every angle is a right angle (90°).
means "right angle"
show equal sides
All sides are equal in length
Each internal angle is 90°
Opposite sides are parallel (so it is a Parallelogram).
Play with a square:
A square also fitsthe definitionof a rectangle (all anglesare 90°), and a rhombus (all
sides are equal length).
2. Area of a Square
The Area is the side length squared:
Area = a2 = a × a
Example: A square has a side length of 6 m, what is its Area?
Area = 6 m × 6 m = 36 m2
The Area is also half of the diagonal squared:
Area =
𝑑2
2
Perimeter of a Square
The Perimeter is the distance around the edge.
The Perimeter is 4 times the side length:
Perimeter = 4a
Example: A square has a side length of 12 cm, what is its Perimeter?
Perimeter = 4 × 12 cm = 48 cm
Diagonals of a Square
A square has two diagonals, they are equal in length and intersect in the middle.
The Diagonal is the side length times the square root of 2:
Diagonal "d" = a × √2
Example: A square has a side length of 5 m, what is the length of a diagonal?
3. Diagonal Length = a × √2 = 5 × 1.41421... = 7.071 m (to 3
decimals)
https://www.mathsisfun.com/definitions/quadratic-equation.html
https://en.wikipedia.org/wiki/Square
