Area and Perimeter of a Triangle: Formula, Examples, and Common Mistakes

After mastering rectangles and squares, the triangle is the next shape most students search for — and for good reason. Triangles show up everywhere, from rooftops to road signs, and their area formula is one of the most tested concepts in school math. In this post, you'll learn the formulas for area and perimeter, see worked examples, and avoid the mistakes students make most often.

What Is a Triangle?

A triangle is a three-sided shape (polygon) with three angles that always add up to 180 degrees. Triangles can look very different from each other — tall and narrow, short and wide, or perfectly symmetrical — but the same core formulas apply to all of them.

To calculate a triangle's area, you need two measurements:

Base (b): any one side of the triangle, usually drawn at the bottom

Height (h): the perpendicular (straight up-and-down) distance from the base to the opposite corner

Area of a Triangle

The area of a triangle tells you how much surface it covers.

Formula:

Area = ½ × base × height

Or simply: A = (b × h) ÷ 2

This formula makes sense once you see where it comes from: a triangle is exactly half of a rectangle (or parallelogram) that shares the same base and height. That's why we multiply base by height, then cut the result in half.

Example 1:

A triangle has a base of 10 cm and a height of 6 cm. Find its area.

• Area = (b × h) ÷ 2
• Area = (10 × 6) ÷ 2
• Area = 60 ÷ 2
• Area = 30 cm²

As always, area is measured in square units (cm², m², ft²).

Perimeter of a Triangle

The perimeter is the total distance around all three sides of the triangle.

Formula:

• Perimeter = side a + side b + side c

Unlike area, the perimeter formula doesn't need base and height — it simply adds up the lengths of all three sides.

Example 2:

A triangle has sides measuring 7 cm, 8 cm, and 9 cm. Find its perimeter.

• Perimeter = 7 + 8 + 9
• Perimeter = 24 cm

Perimeter is measured in linear units (cm, m, ft), just like with rectangles and squares.

Area vs. Perimeter: What's the Difference?

Area:

• What it measures: the space inside the triangle
• Formula: (b × h) ÷ 2
• Unit: square units (cm², m²)
• What you need: base and perpendicular height

Perimeter:

• What it measures: the distance around the triangle
• Formula: a + b + c
• Unit: linear units (cm, m)
• What you need: the lengths of all three sides

In short — area tells you how much space is inside the triangle, while perimeter tells you how far it is around the outside.

Common Mistakes Students Make

1. Using the slanted side instead of the perpendicular height. The height must always meet the base at a 90-degree angle — using a slanted side by mistake gives the wrong area.
2. Forgetting to divide by 2. Since a triangle is half of a rectangle, skipping the "÷ 2" step is one of the most common exam errors.
3. Confusing area and perimeter formulas. Some students try to add the base and height for area, or multiply the three sides for perimeter — both are incorrect.
4. Dropping the square unit for area. Writing "30 cm" instead of "30 cm²" is a frequent mistake in written exams.

Practice Problem

Try this one yourself before checking the answer:

A triangular garden has a base of 14 meters and a height of 9 meters. Its three sides measure 14 m, 11 m, and 13 m. Find both its area and perimeter.

Click to see the answer

• Area = (14 × 9) ÷ 2 = 126 ÷ 2 = 63 m²
• Perimeter = 14 + 11 + 13 = 38 m

Quick Recap

• Area = (base × height) ÷ 2 — measured in square units, using the perpendicular height
• Perimeter = side a + side b + side c — measured in linear units
• Always double-check that your height is perpendicular to the base before calculating area

Now that you've covered rectangles, squares, and triangles, you have the foundation for understanding more shapes — like circles and parallelograms — which build on these same "space inside vs. distance around" concepts.

More read: Area and Perimeter of a Square