# Area of a Square: Worked Examples

One of the word problems involved in Geometry in the Civil Service Examinations is about area. In this series of posts, we are going to discuss sample problems which are typically used in the exams. We start with the easiest problems where we substitute the given to the formulas and then discuss more complicated problems at the end. In this post, we will discuss how to solve problems involving area of a square.

The formula area of a square (A) is the product of the length the sides (s).

$A = s \times s$ or $A = s^2$.

Example 1

The side length of a square is 6 units. What is its area?

Solution

$A = s \times s$

$A = 6 \times 6$

$A = 36$

Therefore, the area of a square is $36$ square units.

Example 2

The area of a square is 144 square units. What is the side length?

Solution

$A = s \times s$

Substituting the given, we have

$144 = s \times s$.

Since $s \times s = s^2$, to get the value of $s$, we have to get the square root of both sides.

$\sqrt{144} = \sqrt{s^2}$

$12 = s$

Therefore, the side length of the square is $12$ units.

Example 3

If the side length of a square is increased by 4, its area increases 80. What is the side length of the square?

Solution

Let $x$ be the side length of the original square. When it is increased by $4$, then its new length is $x + 4$. With this information, we can get the following:

Original area increased by 80: $x^2 + 80$
Area of the new square: $(x + 4)^2$

Now, the original area above increased by 80 is equal to the area of the new square, so we can equate the two expressions above. That is,

$(x + 4)^2 = x^2 + 80$
$x^2 + 8x + 16 = x^2 + 80$.

Subtracting $x^2$ from both sides, we have

$8x + 16 = 80$
$8x = 64$
$x = 8$.

Therefore, the side length of the square is 8 units.

### 1 Response

1. November 20, 2015

[…] the previous posts, we have solved problems on how to calculate the area of square and rectangle. We continue this series by solving problems involving area of […]