Height — Definition, Formula & Examples
Height is the straight-up-and-down distance from the base of a shape or object to its top. It is always measured at a right angle (90°) to the base.
The height (or altitude) of a geometric figure is the perpendicular distance from the base to the opposite vertex or to the highest point of the figure.
How It Works
To find the height of a shape, pick the side you are calling the base, then measure straight up from that base to the very top. The measurement must form a right angle with the base — it cannot be slanted. In a rectangle, the height is simply one of the sides. In a triangle, the height might fall inside or even outside the triangle, depending on its shape. Height is one of the key measurements you need when calculating area or volume.
Worked Example
Problem: A triangle has a base of 10 cm and a height of 6 cm. What is its area?
Identify the measurements: The base is 10 cm and the height is 6 cm. The height is measured perpendicular to the base.
Use the triangle area formula: Area equals one-half times base times height.
Calculate: Multiply to get the area.
Answer: The triangle's area is 30 cm².
Why It Matters
You need height every time you calculate the area of a triangle, parallelogram, or trapezoid. It also shows up in volume formulas for prisms, cylinders, and cones — shapes you will work with throughout elementary and middle school math.
Common Mistakes
Mistake: Using a slanted side of a triangle as the height instead of the perpendicular distance.
Correction: The height must form a 90° angle with the base. In many triangles, the height is not the same as any of the three sides — it is a separate line drawn straight down to the base.