Square | what is Square?
Definition: In geometry, a square is a quadrilateral having its all four
sides equal and each angle 90°.
In the given figure of
quadrilateral ABCD, AB = BC = CD = AD and ∠A = ∠B = ∠C = ∠D = 90°. So ABCD is a
square.
Note:
- A square is also a parallelogram having all sides
equal.
- A square is also a rectangle having all sides equal.
- A square is also a rhombus having all angles 90°.
Length of a square
All four sides of a square are equal and the measure of the side is taken as length (l) of the square. In the given figure of square ABCD,
Length
of square = AB = BC = CD = AD = l
Diagonals of a square
The line joining the opposite vertices of a quadrilateral is
called a diagonal. Two diagonals of a square are equal and bisect to each other
at 90°.
In the given figure, ABCD is a square. AC and BD are diagonals.
They are equal and bisect to each other perpendicularly at point O i.e. AC = BD
and AO = CO = BO = DO.
Length of diagonal of a square is given by the formula:
Perimeter and Area of Square
Perimeter and area of a square are given by the formula:
Perimeter
= 4l, where l is the length of side of square.
Area = l^{2} or ½ d^{2}, where d is
the length of diagonal.
Properties of Square
1.
All sides of square are equal.
2.
Each angle of a square is 90°.
3.
Opposite sides of a square are parallel.
4.
Diagonals of a square are equal.
5.
Diagonals bisect to each other at 90°.
You can comment your questions or problems regarding square here.
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