When weβre asked to find the area of a triangle, what weβre looking for is the amount of space inside the sides of our triangle.

$A=2bhβ$

The formula is pretty straightforward, but correctly identifying the base and the height of the triangle can sometimes be tricky. Thatβs why we like to imagine triangles as mountains!

$b$

$h$

$b$

$h$

Type of Triangle:

We can imagine the triangle as a mountain where the base is flat (β¬), and the height is a vertical line that connects the base to the peak (β¬).

Sometimes, we may need to rotate our triangle in order for it look like a mountain:Check out our calculator or continue the lesson to see some examples in action!

Area of Triangles Calculator

What does your triangle look like?

Step 1. Identify the base and height of the triangle.

Imagine the triangle is a mountain. The base must be flat and the height connects the base of the mountain to the peak.

$b=$

$h=$

Step 2. Multiply the base by the height.

$A=2bΓhβ=20Γ0β=20β$

Step 3. Divide by 2.

$A=20β=0$So, the area of the triangle is $0$.

Recap π§’ How to Find the Area of a Triangle

Step 1. Identify the base and height of the triangle.

Imagine the triangle is a mountain. The base must be flat and the height connects the base of the mountain to the peak.

Step 2. Multiply the base by the height.

$A=2bΓhβ$

Step 3. Divide by 2.

$A=2bΓhβ$

We divide by 2 because the area of a right triangle is equal to Β½ the area of a rectangle$Β(A=lΓw=bΓh)Β$made up of two right triangles with the same base and height.

Continue to see how we can visualize finding the area of a triangle in more detail, starting with right triangles β¨.

You can also use the Quick Links menu on the left to jump to a section of your choice.

Right Triangles

The area of a right triangle is equal to $21β$ the area of a rectangle made up of two right triangles with the same base and height:$AreaΒ ofΒ triangleβ=2AreaΒ ofΒ rectangleβ=2bhββ$

Let's do some practice problems!

We'll start with this triangle:

$5$

$6$

$5$

$6$

Nice work! Now, you might have noticed that right triangles are special because we can choose to make either of the two perpendicular sides of the triangle the base and height. Letβs try an example where we can see this in practice!

Great job! Practice with some additional problems or keep scrolling to learn how to find the area of an acute triangle.

Practice: Area of Right Triangles

Question 1 of 3: Find the area of this triangle β¬οΈ

$3$

$4$

$5$

$3$

$4$

$5$

Step 1. Identify the base and height of the triangle.

Imagine the triangle is a mountain. The base must be flat and the height connects the base of the mountain to the peak.

$b=$

$h=$

Step 2. Multiply the base by the height.

$A$$=$$2bΓhβ$$=$$23Γ4β$$=$

$2$

Step 3. Divide by 2.

$A=212β=$

Nice work! Our answer is $A=6$.

Continue on to see how we find the area of an acute triangle β¨.

Acute Triangles

The area of an acute triangle is equal to $21β$ the area of a parallelogram made up of two acute triangles with the same base and height:$AreaΒ ofΒ triangleβ=2AreaΒ ofΒ parallelogramβ=2bhββ$

When it comes to finding the area of an acute triangle, the height will be shown inside the triangle as a straight or dotted line connecting the base to the peak:Let's try some examples π₯.

We'll start with this triangle:

$3$

$6$

$3$

$6$

Amazing job! Now try another one - and don't get distracted by all the different side lengths π.

$3$

$4$

$5$

$6$

$3$

$4$

$5$

$6$

Nice work! Practice with some additional problems or keep scrolling to see how we find the area of an obtuse triangle.

Practice: Area of Acute Triangles

Question 1 of 3: Find the area of this triangle β¬οΈ

$4$

$5$

$9$

$12$

$4$

$5$

$9$

$12$

Step 1. Identify the base and height of the triangle.

Imagine the triangle is a mountain. The base must be flat and the height connects the base of the mountain to the peak.

$b=$

$h=$

Step 2. Multiply the base by the height.

$A$$=$$2bΓhβ$$=$$24Γ5β$$=$

$2$

Step 3. Divide by 2.

$A=220β=$

Nice work! Our answer is $A=10$.

Continue on to see how we find the area of an obtuse triangle β¨.

Obtuse Triangles

The area of an obtuse triangle is equal to $21β$ the area of a parallelogram made up of two obtuse triangles with the same base and height:$AreaΒ ofΒ triangleβ=2AreaΒ ofΒ parallelogramβ=2bhββ$

When it comes to finding the area of an obtuse triangle, the height will be show outside the triangle, since it needs to be a vertical line connecting the base to the peak:Let's try some examples π₯π₯.

Start with this one:

$6$

$5$

$9$

$7$

$6$

$5$

$9$

$7$

Wow nice job! Try one more:

$4$

$6$

$8$

$5$

$4$

$6$

$8$

$5$

Amazing! Try out these practice problems or scroll down to celebrate completing this lesson!

Practice: Area of Obtuse Triangles

Question 1 of 3: Find the area of this triangle β¬οΈ

$4$

$7$

$11$

$9$

$4$

$7$

$11$

$9$

Step 1. Identify the base and height of the triangle.

Imagine the triangle is a mountain. The base must be flat and the height connects the base of the mountain to the peak.

$b=$

$h=$

Step 2. Multiply the base by the height.

$A$$=$$2bΓhβ$$=$$24Γ7β$$=$

$2$

Step 3. Divide by 2.

$A=228β=$

Nice work! Our answer is $A=14$.

When you feel like you've mastered this lesson, click for a celebration β¬οΈ!

Amazing work, look at you go! Thanks for checking out this lesson βΊοΈπ. Where to next?