The word ‘square’ in mathematics may refer to a square in geometry or the same in algebra. Both meanings are similar in some way and also different in some ways.
For the level of a 4th grader, the word usually refers to a plane shape of four sides as shown in the picture below. This can be called the square in geometry.
Shown above is one such. The properties of the same are as follows:
1. All sides are of equal length.
2. All angles are of equal measures.
3. It is also called a regular four sided polygon.
Some examples of a sq. can be stated as follows:
Any face of a cube is also same. A die used for playing board games is same shape. The base of Egypitian pyramids and the base of the Eiffel tower is also having the same shape.
Perimeter of a square: The perimeter refers to the sum of all the four sides of such figure. If the length of each of the sides of the same is ‘a’ units, then the sum of lengths of all the four sides would be = a + a + a + a = 4a. Thus perimeter of a sq. = 4a units.
Area of a sq. = If each of the sides of the same are ‘a’ units, then the area enclosed by the sq. polygon can be given by the formula:
A = a * a = a^2 sq. units.
Example: Find the area and the perimeter of the following:
Solution: Perimeter = 4a = 4*5 = 20 cm
Area = 5*5 = 5^2 = 25 sq cm.
Sq. value of a number:
In math, another concept for the same is regarding the square of a number. In general, such number refers to the area of a sq. figure such that the said number is the length of each of the side. Therefore if we say that we need the sq. of a number x, then the answer would be equal to the area of the same such that each of the sides of the sq. figure is x. So that would be x * x = x^2.
Finding Square of a number:
For smaller numbers, to find the sq. value is relatively easy. For example sq. value of 2 would be = 2*2 = 4.
Sq. value of 7 is 7*7 = 49 and so on. For larger numbers, it can be found using various methods. Let us try to understand this better using an example.
Example: Find the sq. of the number 13.
Solution: We know that its nothing but 13 * 13
This could be rewritten as:
13^2 = 13*13
= (10+3) * (10+3)
= 10*10 + 10*3 + 10*3 + 3*3 (FOILing the terms)
= 100 + 30 + 30 + 9
= 100 + 60 + 9
= 169 <- answer="" p="">Alternatively, instead of FOILing the terms, we can also use the identity:
(a+b)^2 = a^2 + 2ab + b^2
For the level of a 4th grader, the word usually refers to a plane shape of four sides as shown in the picture below. This can be called the square in geometry.
1. All sides are of equal length.
2. All angles are of equal measures.
3. It is also called a regular four sided polygon.
Some examples of a sq. can be stated as follows:
Any face of a cube is also same. A die used for playing board games is same shape. The base of Egypitian pyramids and the base of the Eiffel tower is also having the same shape.
Perimeter of a square: The perimeter refers to the sum of all the four sides of such figure. If the length of each of the sides of the same is ‘a’ units, then the sum of lengths of all the four sides would be = a + a + a + a = 4a. Thus perimeter of a sq. = 4a units.
Area of a sq. = If each of the sides of the same are ‘a’ units, then the area enclosed by the sq. polygon can be given by the formula:
A = a * a = a^2 sq. units.
Example: Find the area and the perimeter of the following:
Solution: Perimeter = 4a = 4*5 = 20 cm
Area = 5*5 = 5^2 = 25 sq cm.
Sq. value of a number:
In math, another concept for the same is regarding the square of a number. In general, such number refers to the area of a sq. figure such that the said number is the length of each of the side. Therefore if we say that we need the sq. of a number x, then the answer would be equal to the area of the same such that each of the sides of the sq. figure is x. So that would be x * x = x^2.
Finding Square of a number:
For smaller numbers, to find the sq. value is relatively easy. For example sq. value of 2 would be = 2*2 = 4.
Sq. value of 7 is 7*7 = 49 and so on. For larger numbers, it can be found using various methods. Let us try to understand this better using an example.
Example: Find the sq. of the number 13.
Solution: We know that its nothing but 13 * 13
This could be rewritten as:
13^2 = 13*13
= (10+3) * (10+3)
= 10*10 + 10*3 + 10*3 + 3*3 (FOILing the terms)
= 100 + 30 + 30 + 9
= 100 + 60 + 9
= 169 <- answer="" p="">Alternatively, instead of FOILing the terms, we can also use the identity:
(a+b)^2 = a^2 + 2ab + b^2
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