The formula for calculating the area of a triangle of any type:
height times base divided by .
How to find the area of a triangle:
![A3 - the general formula for calculating the area of triangles](/_ipx/f_png,s_500x242/https://cdn.tutorela.com/images/A3_-_the_general_formula_for_calculating_the_a.width-500.png)
The formula for calculating the area of a triangle of any type:
height times base divided by .
What is the area of the given triangle?
Information:
If we apply the formula, we multiply the height ( cm) by the length of the base ( cm).
By multiplying by , we obtain , a result that we must divide by .
divided by equals .
The area of this triangle is therefore: .
Whether you are preparing for an test or are about to take your university entrance exams, it is essential to know how to calculate the area of a triangle, whether it is right angled, isosceles, etc.
So, how do you calculate a triangular area? This guide will clear up all of your doubts concerning one of the most frequently asked questions in geometry examinations.
Calculate the area of the triangle using the data in the figure below.
Calculate the area of the triangle using the data in the figure below.
Calculate the area of the triangle using the data in the figure below.
A triangle is a geometric figure composed of three sides that form three angles and three vertices.
The vertices of the triangle are marked with the letters and ; together creating the sides: .
There are different types of triangles and some of them even share characteristics. We will deal with those later in this article!
Before addressing the different types of triangles that exist and how to calculate their areas,
we must first know the terms that are usually used when we talk about a triangular area.
Calculate the area of the triangle using the data in the figure below.
Complete the sentence:
To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.
Calculate the area of the triangle below, if possible.
One of the most useful tips when calculating the area of a triangle (and thus solving the problem) is to understand that a triangle is a half-square.
There are triangles that are easily distinguishable as "half-squares" because of their shape, such as the isosceles right triangle.
However, it is important to note that triangles that do not appear to be "half-squares" are also "half-squares", since this is one of the features that characterize them.
What is the next step?
Calculate the area of the triangle.
The formula used to calculate the area of a triangle is as follows:
height times base divided by .
Information:
Solution:
If we apply the formula, we multiply the height ( cm) by the length of the base ( cm).
By multiplying by , we get , a result that we must divide by .
divided by equals .
The area of this triangle is therefore: .
Calculate the area of the triangle below, if possible.
Calculate the area of the following triangle:
Calculate the area of the following triangle:
Information:
Solution:
Again, if we apply the formula, we multiply the height ( cm) by the length of the base ( cm).
By multiplying by , we get , a result that we must divide by .
divided by equals .
Therefore, the area of this triangle is: .
Information:
Solution:
If we apply the formula, we multiply the height ( cm) by the length of the base ( cm).
By multiplying by we get , a result that we must divide by .
by equals .
Therefore, the area of this triangle is cm².
By clicking on the link you can find more information about a scalene triangle
Calculate the area of the following triangle:
Calculate the area of the following triangle:
Calculate the area of the triangle ABC using the data in the figure.
Information:
Note: in a right triangle or right-angled triangle, the base and the height correspond to the legs of the triangle.
Solution:
If we apply the formula, we multiply the height ( cm) by the length of the base ( cm).
By multiplying by we get , a result that we must divide by .
by equals .
Therefore, the area of this triangle is: .
Information:
Please note:
In an obtuse triangle, the height is outside the triangle.
This means that we must extend the line of the base from point to the point to find the height.
In this way we create a right triangle ,where the height we are looking for is the side .
However, remember that since we are trying to calculate the area of the obtuse triangle, we only have to consider the side as the base. is the base.
Solution:
In this case, if we apply the formula, we multiply the height ( cm) by the length of the base of the triangle whose area we want to find.
By multiplying by we obtain , a result that we must divide by .
divided by equals .
Therefore, the area of this triangle is: .
Calculate the area of the right triangle below:
What is the area of the triangle in the drawing?
What is the area of the given triangle?
What is Heron's formula and what is it for?
Heron's formula, the invention of which is attributed to the Greek mathematician Heron of Alexandria, allows us to obtain the area of a triangle knowing the lengths of its three sides and .
Where 's' is the perimeter of the triangle divided by :
Task:
In the grounds of a hotel, they want to build a special triangular-shaped pool.
The length of the pool is m.
The width of the pool is m.
The pool is to be covered with tiles m long and m wide.
Question:
How many tiles are needed to cover the pool area?
Solution:
To find out how many tiles are needed, we must calculate the triangular area of the pool and the area of each tile, then divide these numbers.
The result is equal to the number of tiles needed.
In a triangle, its length is equal to its height and its width is equal to the base of the triangle.
h = length = meters.
base = width = meters.
Since the length is meters, the width is also meters.
Tile area:
Answer:
tiles
Calculate the area of the triangle using the data in the figure below.
Calculate the area of the triangle using the data in the figure below.
Calculate the area of the triangle using the data in the figure below.
Task:
The triangle is a right-angled triangle.
The area of the triangle is equal to .
Calculate and the length of the side .
Solution:
We use the formula to calculate the area of the right triangle:
Then compare the expression with the area of the triangle ().
Multiplying the equation by the common denominator means that we multiply by .
We open the parentheses before the distributive property:
/
/
Replace into the expression and we find:
Answer:
Task:
Given the triangle , calculate the height .
The length of the side is equal to .
The area of the triangle is equal to cm².
Solution:
We use the formula to calculate the area of the triangle.
Please note: in the obtuse triangle, the height is outside of the triangle!
Double the equation by a common denominator.
/
Divide the equation by the coefficient of .
/
Answer:
The length of the height is equal to .
Calculate the area of the triangle using the data in the figure below.
Complete the sentence:
To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.
Calculate the area of the triangle below, if possible.
Task:
Given the right triangle , calculate the area of the triangle. .
The perimeter of the triangle is equal to .
Given: .
Solution:
Given that the perimeter of the triangle is equal to , we can calculate
/
Now we can calculate the area of the triangle .
Please note: we are talking about an obtuse triangle, so its height is .
We use the formula to calculate the area of the triangle:
Answer:
The area of the triangle is equal to .
The triangle is isosceles. Therefore, .
is the height from the side .
Since , the length of the height is percent longer than the length of the side .
Task:
Calculate the area of the triangle .
Solution:
Since it is an isosceles triangle (and, therefore, median), and .
The height is percent longer than the length of .
That is:
Hence, the area of the triangle :
Answer:
The area of the triangle is equal to .
Calculate the area of the triangle below, if possible.
Calculate the area of the following triangle:
Calculate the area of the following triangle:
The rest of the terms, such as median, bisector, etc., are used when we are missing some data. These terms help us to find new data when we have to solve a problem in which we are missing information.
Many students experience a sense of failure when they don't do as well in their exams as they would have liked. However, success in this regard is subjective. Instead of comparing yourself with your peers, you must take into consideration your own achievements and leave aside the results of your classmates. Often, the problem is not that you did not know something or that you did not understand how to calculate the area of a triangle, but rather that you did not prepare well for the exam.
To give an example: imagine an excellent pastry chef who knows many recipes, knows the products and succeeds in creating truly delicious pastries. If he had not practiced and had not prepared well (buying the products and appliances he needs, finding good recipes and having patience with the right timing, etc.), he would not have achieved good results. This is also true for students—good preparation is key!
Calculate the area of the following triangle:
Calculate the area of the following triangle:
Calculate the area of the triangle ABC using the data in the figure.
Your study skills are as important as learning the subject matter. For this reason, a stopwatch can be your great ally. We recommend that you adopt its use from now on. The one that often comes with a cell phone is more than enough!
Once you have studied a subject area, it is advisable to practice and solve problems with a stopwatch, even when you are not preparing for exams. Why?
Calculate the area of the right triangle below:
What is the area of the triangle in the drawing?
What is the area of the given triangle?
Many students have a hard time digesting the fact that they got a low grade and, more importantly, the disappointment that often accompanies it. It is very important for you to know that the more you let this affect you, the worse the impact on your academic achievement will be.
The grade you get on an exam is a kind of feedback that tells you what you are doing well and what you could improve. How can this feedback change the way you study?
We do not recommend it and the reason is very simple: a private lesson is "private", that is to say, it is adapted to your needs. When two friends study in the same private class, one of them will have to adapt to the rhythm of the other.
Thus, the idea of tailoring a "private lesson" to the student's needs is diluted. That said, if both you and your friend find the same topic difficult (for example, how to calculate the area of a triangle), you can take a joint private lesson.
Calculate the area of the triangle using the data in the figure below.
Calculate the area of the triangle using the data in the figure below.
Calculate the area of the triangle using the data in the figure below.
If the question asks about a right triangle, you can multiply the legs (the sides of the triangle that are not the base) and divide by 2. This method is often a great shortcut to reaching the solution. That is why it is important that you know the formula and this specific feature of this triangle.
Also, if you are asked about an isosceles triangle, you should know that both the bisector and the median are considered the height of the triangle. With this knowledge, you can quickly work out the area of the triangle.
If you are interested in learning how to calculate areas of other geometric shapes, you can enter one of the following articles:
In Tutorela you will find a variety of articles about mathematics!
Calculate the area of the triangle using the data in the figure below.
Complete the sentence:
To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.
Calculate the area of the triangle below, if possible.
Many times, the study of mathematics arouses some anxiety among students in high school and further education. A private math class is ideal for those who want to get good grades on their exams, but don't know how.
A private lesson focuses on a certain aspect and includes more than just doing exercises, like:
In the past, private lessons in mathematics or any other subject took place at the student's or teacher's home. Nowadays, it is also possible to have private lessons online. This offers a great way to learn advanced subject from the comfort of your own home, at the hours that best suit both the student and the teacher.
Triangles and other geometric shapes are aspects that students are exposed to as early as their first years in high school. Their grades in mathematics are what set the pace of their learning and can affect whether or not a student chooses to continue studying the subject at later on. Often, what holds people back when studying mathematics is not based on intelligence or aptitude, but rather arises from erroneous learning methods that do not help the student understand the subject matter effectively. A private mathematics teacher works side by side with the student, ensuring that in the end the student has understood their lessons.
Calculate the area of the triangle below, if possible.
Calculate the area of the following triangle:
Calculate the area of the following triangle:
What is the area of the given triangle?
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:
15
Calculate the area of the triangle below, if possible.
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.
Cannot be calculated
Calculate the area of the following triangle:
The formula for the area of a triangle is
Let's insert the available data into the formula:
(7*6)/2 =
42/2 =
21
21
Calculate the area of the following triangle:
The formula for calculating the area of a triangle is:
(the side * the height from the side down to the base) /2
That is:
We insert the existing data as shown below:
10
Calculate the area of the triangle ABC using the data in the figure.
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:
36 cm²