Altitude of a Triangle: Definition, Examples, Chart, and Practice

What is the altitude of a triangle?

The altitude of a triangle is the triangle height.

It starts at a vertex and meets the opposite side at a right angle.

The right angle is important. A slanted side is not the height unless it is perpendicular to the base.

Altitude rule

Use this rule when you look for the height of a triangle.

An altitude is perpendicular to the base.

Perpendicular means the altitude and the base meet at 90°.

Altitude chart

A triangle can have different-looking altitudes.

The altitude may be inside the triangle, on a side of a right triangle, or outside the triangle if the triangle is obtuse.

Altitude and triangle area

The altitude is the height used in the triangle area formula.

Area = 1/2 × base × height

Because the altitude is perpendicular to the base, it gives the straight-up-and-down height needed for area.

The same perpendicular height idea appears later in angle of depression problems, where height and distance also make a right triangle.

Worked example

Problem: A triangle has a base of 12 cm and an altitude of 7 cm. What is its area?

Step 1: Use Area = 1/2 × base × height.

Step 2: Substitute the numbers: Area = 1/2 × 12 × 7.

Step 3: 12 × 7 = 84, and half of 84 is 42.

Answer: The area is 42 square centimeters.

How to find an altitude in a diagram

Step 1: Choose the base of the triangle.

Step 2: Look at the opposite vertex.

Step 3: Draw or find the line from that vertex that meets the base at 90°.

Step 4: Use that perpendicular length as the height.

Common mistakes

Do not use a slanted side as the altitude unless it meets the base at a right angle.

Do not forget that an obtuse triangle may have an altitude outside the triangle.

Do not use the base length as the height. Base and height are different measurements.

Quick practice

1. A triangle altitude must meet the base at 90°.

2. If the base is 10 and the altitude is 6, the area is 30 square units.

3. If the height line is slanted and not perpendicular, it is not the altitude.

4. A right triangle can use one leg as the base and the other leg as the altitude.