Pengi Editor's Note: This article was originally published by Think Academy. We're sharing it here for educational value. Think Academy is a leading K-12 math education provider.
Area of Triangles: Definition, Formula And Examples
Triangles might look simple, but they’re some of the most powerful shapes in math and engineering—used in bridges, buildings, and even art. In this guide, you’ll learn how to identify different types of triangles, understand base and height, and master the area formula with clear examples.
Want extra practice? Scroll down to download free printable worksheets!
Definition of a Triangle
A triangle is a polygon with three angles and three sides. That’s it! But don’t let its simplicity fool you—triangles come in many different types, and some of them are especially useful in math and science.
Let’s explore how to classify triangles and figure out which sides to use as base and height.
Triangle Classification & Find Their Base and Height
Before we jump into triangle area, it’s super helpful to know how to classify triangles. Triangles come in different shapes and sizes, but every triangle has a base (the bottom side we choose to work with) and a height (how tall the triangle is from that base, straight up at a right angle).
Let’s look at two ways to classify triangles—and how to find their base and height in each one!
Classifying by Sides
- Equilateral Triangle
All three sides are equal, and each angle is 60°. You can choose any side as the base. The height drops from the top corner straight down to the middle of the opposite side. It forms a perfect right angle!
- Isosceles Triangle
This triangle has two equal sides and two equal angles. The unequal side is usually picked as the base. The height goes straight down from the top point (between the two equal sides) to the base, cutting it in half.
- Scalene Triangle
All three sides are different lengths. You can choose any side as the base, but be careful! The height must be perpendicular (straight up at a right angle) from the opposite corner to that base. Sometimes you even have to draw the height outside the triangle!
Classifying by Angles
- Acute Triangle
All three angles are less than 90°. Any side can be the base. Draw the height from the opposite corner straight down so it forms a right angle with the base—inside the triangle.
- Right Triangle
One angle is exactly 90°. The two sides that form the right angle are perfect to use as the base and height!
- Obtuse Triangle
One angle is greater than 90°. You usually use the side opposite the obtuse angle as the base—that’s the easiest choice! But if you choose a different side as the base, the height will fall outside the triangle. You’ll need to look closely and draw carefully to find the right perpendicular height.
No matter the triangle type, as long as you have the base and a height that’s perpendicular to it, you’re ready to use the area formula!
Triangle Area Formula: Where It Comes From
Now, let’s talk about how to find the area of a triangle!
1. Make a Copy of the Triangle
First, take your triangle and make an identical copy of it.
2. Rotate and Combine the Two Triangles
Now, rotate the copy and place it next to the original triangle, matching their sides.
Surprise! The two triangles now form a brand-new shape—a parallelogram!
3. Understand the Parallelogram’s Base and Height
In this new parallelogram, the base is the same as the base of the triangle.
The height stays the same too—it’s the straight-up distance from the bottom to the top. These two parts are the key to finding area.
4. Use the Parallelogram Area Formula
You may already know the area of a parallelogram is:
Area of the Parallelogram = base × height
Since we used two triangles to make this parallelogram, each triangle must be half of the total area.
5. Find the Triangle’s Area
So now we can write the triangle’s area like this:
Area of the triangle = ½ × Area of the parallelogram = ½ × base × height
That’s the famous triangle area formula!
Area = ½ × base × height
It works for every triangle, as long as you know the base and the height.
Example: Applying the Triangle Area Formula
Example 1
Problem:
What is the area of this equilateral triangle with side length 4?
Answer
Given Base = 4, Height = 5
Area of the triangle = ½ × base × height = ½ × 4 × 5 = 10
Example 2
Problem:
What is the height of this isosceles right triangle with area 8?
Answer:
For isosceles right triangle, base = height
Let’s set base = height = a
Area of the Triangle = ½ × base × height = ½ × a × a = 8
a × a = 16
a = 4
The height of this triangle is 4.
Want more practice with triangle area?
Wrapping Up the Triangle Area Formula
Now that you know the magic of triangles, try using what you’ve learned! Draw, build, explore—and see how triangles make the world stronger, smarter, and more fun. Math adventure awaits!
To help you see how triangles fit into the big picture of geometry, here’s a quick summary of the area formulas for some common shapes:
| Shape | Figure | Area Formula | Special Notes |
|---|---|---|---|
| Square |  | Area = side² | All four sides are equal |
| Rectangle |  | Area = length × width | Opposite sides are equal |
| Triangle |  | Area = ½ × base × height | Three sides |
| Parallelogram |  | Area = base × height | Opposite sides are parallel |
| Trapezoid |  | Area = ½ × (base₁ + base₂) × height | One pair of parallel sides |
Even More Math Worksheets for Practice!
We’ve created a full library of printable resources — from foundational math to logic-based challenges — organized by grade to support every stage of your child’s journey.
Additional Math Topics for Grade 6 – with Free Worksheets
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