By what percentage will the area of the square increase if its length of the sides is increased by 10%

To solve this problem, remember that the area of ​​a square is equal to the square of its side. S = a ^ 2. Let the side of the square be – a. Then the area of ​​the square.
S = a ^ 2.
Let’s enlarge the side by 10%. In order to find the percentage of the number, you need to multiply this number by the percentage and divide by one hundred.
a + 10/100 * a = a + 0.1a = 1.1a.
Let’s calculate the area of ​​a square with a side of 1.1a.
S = (1.1a) ^ 2 = 1.21a ^ 2.
To find how many percent one number is from another, you need to find the quotient of these numbers, and then translate it into percentages (for this, multiply the resulting number by 100%).
1.21a ^ 2 – a ^ 2 = 0.21a ^ 2.
Let’s calculate by what percentage the area has increased.
0.21a ^ 2 / a ^ 2 * 100 = 0.21 * 100 = 21%.
Answer: 21%.