(Continued from above)Properties and important points to remember-
• A square can is also a rectangle with all sides equal, or a rhombus with all
angles equal, or a parallelogram having equal diagonals that bisect the angles.
• Opposite sides of a square are both parallel and equal.
• The diagonals of a square are perpendicular bisector of each other i.e. one cuts
the other into two equal halves and form right angle i.e.
90°angle at intersection point.
• Notice that if a figure is both a rectangle i.e. having right angles;
and a rhombus having equal edge lengths, then it is a square.
• In case of a rhombus if the diagonals are equal, then it must be a square.
Each diagonal length of a square is 2 times the length of the side of the square.
• The area of a square is s2, where‘s’ is the length of one side.
• The length of each diagonal is s2, where‘s’ is the length of any one side.
The area of a square- given length of the diagonals (d) is half times the
product of diagonals.
As both diagonals are congruent ():
Area= (d)2/2, where‘d’ is the length of either diagonal.
• If a circle is circumscribed around a square, the area of
the circle is
/2 times the area of the square.
• If a circle is inscribed in the square, the area
of the circle is
/4 times the area of the square.
• A square has larger area than any other quadrilateral having the same perimeter.
Example5: Given- find the area of square ABCD
in the figure given below:
Step 1: Refer to the figure given below. Notice that side of the square DC
is 5 cm.
Step 2: Use the formula A= s2
Step 3: A = 52 = 25
The area of a square ABCD is 25 cm2, as the final answer.
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90°angle at intersection point.
2 times the length of the side of the square.
):
Area= (d)2/2, where‘d’ is the length of either diagonal.
