Area of a Triangle

Lesson Objective

In this lesson, we will learn about the area of a triangle.

Study Tips

Tip #1 - Area Formula

A triangle is a three sided polygon. Consider a triangle with the base b and the height h. With this, the area A, of this triangle will be:

Note that, this formula only works if the triangle's height is perpendicular to its base. The study tip and math video below will explain more.

Tip #2 - Example Triangles

Now, to use this formula, we have to make sure that the height of the triangle is perpendicular to its base. The pictures below show three triangles with their respective base b and height h:

Acute Triangle

Right Triangle

Obtuse Triangle

Math Video

Lesson Video

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Math Video Transcript

00:00:03.230
In this lesson, we will learn about the area of a triangle.

00:00:08.100
First, let's consider this parallelogram with the base B and the height H.

00:00:15.060
Now, in the previous lesson, we learned that the area of a parallelogram, A = BH.

00:00:22.220
Observe that, if we cut this parallelogram by half, and remove this portion, we now have a triangle with the base B and height H.

00:00:33.210
Since the area of this triangle, is half of the area of a parallelogram, the formula for the area of this triangle, A = 1/2BH.

00:00:45.080
Note that, it is very important to include the unit. Since this is the formula for area, its unit will be in the form of square unit.

00:00:55.050
We will see more explanations on this, in the upcoming example.

00:01:00.140
Now, let's see some examples on using this formula.

00:01:05.070
Find the area of this triangle when its base is 5cm, and its height is 4cm.

00:01:13.020
First, we start with the formula for the area of a triangle, A = 1/2BH.

00:01:20.040
Since the base is given as 5cm, we can substitute B with 5.

00:01:26.240
Similarly, since the height is given as 4cm, we can substitute H with 4.

00:01:34.120
Next, we can simplify by multiplying 5, with 4. This gives 20.

00:01:42.070
Note that, one half bracket 20, can be rewritten as, 1 bracket over 2.

00:01:49.220
Let's continue. 1 multiply 20, gives back 20.

00:01:55.140
20 divides by 2, gives 10.

00:01:59.140
Note that, this number has no meaning unless we include the unit for it.

00:02:04.170
Since the units are given in centimeter, the unit for the area will be in square centimeter.

00:02:11.140
Hence, the area of this triangle is 10 square centimeter.

00:02:17.200
Next example, given that the area of this triangle is 24 square feet, and its base is 6ft. Find its height.

00:02:27.070
Again, we start with the formula for the area of a triangle, A  = 1/2BH.

00:02:34.030
Now, since the area, and the base are given, we can find the height by solving this equation for h. Here’s how.

00:02:43.110
It is easier to work with this equation if we rewrite this term, one half BH as, 1 BH over 3. 1BH is the same as BH.

00:02:55.020
Next, note that we can remove this fraction, by multiplying both sides of the equation with 2.

00:03:02.050
By doing so, we have, 2A = BH.

00:03:07.080
Next, since the area  is given as 24, we can substitute 'A' with 24.

00:03:14.050
2 multiply by 24, gives 48.

00:03:19.000
Similarly, since the base is given as 6 feet, we can substitute B with 6.

00:03:26.020
Now we have, 6h equals to 48.

00:03:30.070
Let's rewrite this equation so that it will look neater.

00:03:30.070
To find h, we need to remove 6. We can do so by dividing both sides of the equation with 6.

00:03:42.120
By doing so, we have, H equals to 48 over 6.

00:03:47.180
48 divides by 6, gives 8.

00:03:52.000
Now, this number is meaningless unless we include the unit for it.

00:03:56.240
Since the base is in feet, the height of the triangle will be in feet.

00:04:02.040
Therefore, the height of this triangle is 8ft.

00:04:07.120
That is all for this lesson. Try out the practice question to further your understanding.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on the area of a triangle or pick your choice of question below.

Question 1 on finding the area of a triangle
Question 2 on finding the height of a triangle

Site-Search and Q&A Library

Please feel free to visit the Q&A Library. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there.

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