# Area of Equilateral Triangles

🏆Practice triangle area

Formula to calculate the area of an equilateral triangle:

## Test yourself on triangle area!

What is the area of the given triangle?

## Area of an Equilateral Triangle

Calculating the area of an equilateral triangle is quite simple, you can't get too confused with it, not even a little.
All you need to remember is the formula we will present to you below and apply it to equilateral triangles:

Remember!
In equilateral triangles, the height is also the median and the bisector.
Therefore, if the question only gives the length of the median or the bisector, you can immediately deduce that it is the height you need to place in the formula.
And on top of that, since the triangle is equilateral, you can immediately find the length of the edge (or side) corresponding. Simply compare it with the given edge since they are all equivalent.

Let's practice so we can understand even better how to calculate the area of an equilateral triangle:

### Let's start with a classic exercise for beginners.

Given the triangle $\triangle ABC$

Given that:
$ABC$ Equilateral triangle
$AD=3$ Height
$CB= 6$

What is the area of the triangle?

Solution:
At first glance, we see that we have a height equivalent to $3$ and a side equivalent to $5$.

Let's put it in the formula and we will obtain:
$\frac{6\times3}{2}=9$

Answer:

The area of the triangle $ABC$ is $9$ cm2.

Simple and easy, right?

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### Now let's move on to a more complicated exercise.

that covers various hypothetical situations that could confuse you on the exam:

Given the equilateral triangle $\triangle ABC$

Given:
$AC = 6$
$DB=AD$
$CD=7$

What is the area of the triangle $\triangle ABC$?

Solution:

We know that to calculate the area of the triangle, we need to have the length of the height and the corresponding side with which it forms $90^o$ degrees.

In this exercise, it is not explicitly stated that $CD$ is the height of the triangle, but we know that: $AD =DB$ that is, $CD$ is the median - it crosses the side it touches, dividing it into two equal parts.
Since it is an equilateral triangle, the median is also the height of the triangle, and therefore, we can use it in the formula for calculating the area.
Additional note: If instead of the data that $CD$ is the median, they had given that it is the bisector $ABC$, we could also have deduced that it is the height, since in an equilateral triangle, the median, the height, and the bisector coincide.

Therefore, we will note $CD=7$ as the height of the triangle.

Now we must find the length of the side $AB$
Since it is an equilateral triangle, all sides are equal, so we immediately deduce that $AB=AC = 6$
Now let's put it in the formula and we will get:

$\frac{6\times7}{2}=21$

Answer:
The area of the triangle $ABC$ is $21$ cm2.

## Examples and exercises with solutions for calculating the area of an equilateral triangle

### Exercise #1

What is the area of the given triangle?

### Step-by-Step Solution

This question is a bit confusing. We need start by identifying which parts of the data are relevant to us.

Remember the formula for the area of a triangle:

The height is a straight line that comes out of an angle and forms a right angle with the opposite side.

In the drawing we have a height of 6.

It goes down to the opposite side whose length is 5.

And therefore, these are the data points that we will use.

We replace in the formula:

$\frac{6\times5}{2}=\frac{30}{2}=15$

15

### Exercise #2

Calculate the area of the triangle below, if possible.

### Step-by-Step Solution

The formula to calculate the area of a triangle is:

(side * height corresponding to the side) / 2

Note that in the triangle provided to us, we have the length of the side but not the height.

That is, we do not have enough data to perform the calculation.

### Answer

Cannot be calculated

### Exercise #3

Calculate the area of the following triangle:

### Step-by-Step Solution

The formula for the area of a triangle is

Let's plug in the data we have into the formula:

(7*6)/2 =

42/2 =

21

21

### Exercise #4

Calculate the area of the following triangle:

### Step-by-Step Solution

The formula for calculating the area of a triangle is:

(the side * the height from the side down to the base) /2

That is:

$\frac{BC\times AE}{2}$

Now we replace the existing data:

$\frac{4\times5}{2}=\frac{20}{2}=10$

10

### Exercise #5

Calculate the area of the triangle ABC using the data in the figure.

### Step-by-Step Solution

First, let's remember the formula for the area of a triangle:

(the side * the height that descends to the side) /2

In the question, we have three pieces of data, but one of them is redundant!

We only have one height, the line that forms a 90-degree angle - AD,

The side to which the height descends is CB,

Therefore, we can use them in our calculation:

$\frac{CB\times AD}{2}$

$\frac{8\times9}{2}=\frac{72}{2}=36$

### Answer

36 cm²

Do you know what the answer is?
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