Area of Triangles Formula
The area of a triangle is half the product of its base and height: A = (1/2)bh.
The Formula
When to use: Every triangle is exactly half of a rectangle with the same base and height — cut the rectangle along the diagonal.
Quick Example
Notation
What This Formula Means
The area of a triangle is half the product of its base and height: .
Every triangle is exactly half of a rectangle with the same base and height — cut the rectangle along the diagonal.
Worked Examples
Example 1
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First step
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Example 2
mediumExample 3
mediumCommon Mistakes
- Forgetting the - a triangle is half a rectangle, so always halve the base-times-height product.
- Using a slanted side instead of the perpendicular height - the height must form a right angle with the base.
- Reporting the answer without square units - area is always in square units (cm², in²).
Why This Formula Matters
It is the foundation for parallelogram, trapezoid, and composite-figure area, and it forces the key habit of using the perpendicular height, not a slanted side. Get the half and the perpendicularity right here, and every later area formula falls into place; miss them, and the errors compound. Recognizing it by "Do I have a base and a height that meets it at a right angle, and do I remember to take half?" — rather than by familiar numbers — is what lets a student tell it apart from area of a rectangle/parallelogram and perimeter of a triangle and pythagorean theorem in a mixed problem set.
Frequently Asked Questions
What is the Area of Triangles formula?
The area of a triangle is half the product of its base and height: .
How do you use the Area of Triangles formula?
Every triangle is exactly half of a rectangle with the same base and height — cut the rectangle along the diagonal.
What do the symbols mean in the Area of Triangles formula?
= base, = height (perpendicular to base), = area
Why is the Area of Triangles formula important in Math?
It is the foundation for parallelogram, trapezoid, and composite-figure area, and it forces the key habit of using the perpendicular height, not a slanted side. Get the half and the perpendicularity right here, and every later area formula falls into place; miss them, and the errors compound. Recognizing it by "Do I have a base and a height that meets it at a right angle, and do I remember to take half?" — rather than by familiar numbers — is what lets a student tell it apart from area of a rectangle/parallelogram and perimeter of a triangle and pythagorean theorem in a mixed problem set.
What do students get wrong about Area of Triangles?
The procedure for area of triangles is the easy part; the trap is forgetting the . Asking "Do I have a base and a height that meets it at a right angle, and do I remember to take half?" first is what keeps a correct-looking calculation from being attached to the wrong concept.
What should I learn before the Area of Triangles formula?
Before studying the Area of Triangles formula, you should understand: area, triangles, multiplication.