Compare the area of a square with a perimeter of 12 cm and a rectangle 3 cm wide and 4 cm long.

| May 25, 2021 | education

Let us denote through the variable S1 the value of the area of ​​our square, through the variable S2 the value of the area of ​​our rectangle, through the variable P the value of the perimeter of our square, equal to 12 cm, through the variable A the value of the length of our square, through the variable B the value of the length of the first side of our rectangle, equal to 3 cm , and through the variable C the value of the length of the second side of our rectangle, equal to 4 cm.

Let’s find the value of the side length of our squares from the following formula.

P = 4 x A.

A = P: 4.

A = 12: 4.

A = 3 cm.

We get that the length of the side of our square is 3 cm.

Let’s find the value of the area of ​​our square using the following formula.

S1 = A ^ 2.

S1 = 3 ^ 2.

S1 = 9 cm ^ 2.

Let’s find the value of the area of ​​our rectangle using the following formula.

S2 = B x C.

S2 = 3 x 4.

S2 = 12 cm ^ 2.

Let us now compare the obtained values ​​of S1 and S2.

Since 12 cm ^ 2 is more than 9 cm ^ 2, we get that S2 is 3 cm ^ 2 larger than S1, and, therefore, that the area of ​​our rectangle is larger than the area of ​​our square by 3 cm ^ 2.



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