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How to Find the Area of a Triangle (Mathematics Lesson)

How to Find the Area of a Triangle

The area of a triangle is found using the formula:



In this formula, b is the length of the base of the triangle and h is the height of the triangle. The image below shows what we mean by the lengths of the bases and the height:

A Real Example of How to Find the Area of a Triangle

An Example Question

What is the area of a triangle with a base of 5 cm and a height of 3 cm, as shown below?

Step 1
Start with the formula:
Area = ½bh
Don't forget: ½bh = ½ × b × h

Step 2
Substitute the length of the base and the height into the formula. In our example, b = 5 and h = 3.
Area = ½ × 5 × 3 = 7.5 cm2
Don't forget: ½ × a number = 0.5 × a number = a number ÷ 2.

The area of the triangle with a base of 5 cm and a height of 3 cm is 7.5 cm2.

Another Real Example of How to Find the Area of a Triangle

The slider below shows another real example of how to find the area of a triangle:

How to Find the Area of a Triangle Using Trigonometry

The area of a triangle can also be found using trigonometry.

The area is found using the formula:



In the formula, a and b are lengths of two sides of the triangle and C is the angle between them. The image below shows what we mean by the two sides and the angle between them:



Read more about how to find the area of a triangle using trigonometry

Curriculum
Geometry Lessons
Interactive Widget
Here is an interactive widget to help you learn about finding the area of a triangle.
Interactive Test
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Here's a second test on finding the area of a triangle.
Here's a third test on finding the area of a triangle.
Note

What Is a Triangle?

A triangle is a flat shape with three straight sides and three corners (also called vertices).

There are different types of triangle:

What's in a Name?

A triangle has three corners and so three angles.

Just as a tricycle has three wheels, and a tripod has three legs, a shape with three angles in called a triangle.

Areas of Triangles and Rectangles

The area of a triangle is ½bh.

The area of a rectangle is bh.

The area of the triangle is half that of the rectangle with the same base length and height.

Can you see from the image of a right-angled triangle below that this is the case?


What about this triangle below?