Square
A square is a special type of quadrilateral, a four-sided polygon, with all sides of equal length and all angles of 90 degrees. This means that all the sides are the same length and all the angles are right angles.
Properties of a Square
- Equal sides: All four sides of a square are of equal length.
- Right angles: All four angles of a square are right angles (90 degrees).
- Diagonals: The diagonals of a square are of equal length and bisect each other at right angles.
- Perimeter: The perimeter of a square is the sum of all its four sides, given by the formula: Perimeter = 4 x side length.
- Area: The area of a square is given by the formula: Area = side length x side length or Area = side length2.
Formulas for Square
Here are the important formulas related to a square:
- Perimeter of a square: P = 4s (where P is the perimeter and s is the length of a side)
- Area of a square: A = s2 (where A is the area and s is the length of a side)
Example Problems
Let's solve a couple of example problems to understand how to use the formulas for a square.
Example 1: Find the perimeter and area of a square with side length 5 cm.
Perimeter = 4 x 5 = 20 cm
Area = 52 = 25 cm2
Example 2: If the area of a square is 49 square units, find the length of each side.
Area = s2 = 49
s = √49 = 7 units
Practice Problems
Now, it's time to practice solving some problems related to squares. Try solving the following problems:
- Find the perimeter of a square with side length 8 cm.
- Calculate the area of a square with side length 12 meters.
- If the perimeter of a square is 20 units, find the length of each side.
By understanding the properties and formulas for squares, you can solve various problems related to this topic. Good luck with your practice problems!
