## 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.

## How to Calculate the Area of a Triangle Part 2

We continue our discussion on how to find the area of a triangle. In the previous post, we have learned where the formula for the area of a triangle came from. We have studied that a triangle with area $A$, base $b$ and height $h$ is

$A = \displaystyle \frac{bh}{2}$

We continue our discussion with the third example in this series.

Example 3

What is the base of a height 7 and area 8.75 square centimeters?

Solution

$A = \displaystyle \frac{bh}{2}$

$8.75 = \displaystyle \frac{b(7)}{2}$

Multiplying both sides by 2, we have  » Read more

## Calculating Areas of Geometric Figures

Area of geometric figures are very common in Civil Service Exams and also other types of examinations. Area is basically the number of square units that can fit inside a closed region. In a closed region, if all the unit squares fit exactly, you can just count them and the number of squares is the area. For example, the areas of the figures below are 4, 10, 8 and 20 square units.

The figures blow are rectangles (yes, a square is a rectangle!). Counting the figures and observing the relationship between their side lengths and their areas, it is easy to see that the area is equal to the product of the length and the width (Why?). » Read more