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"Slant Height" Explained

For pyramids and cones the slant height is the slanted height of the face. Found with pythagorean theorem applied to height and generally half of the base.

Key Idea: Slant Height

For pyramids and cones, the slant height is the distance along the face from the base to the apex (tip).

General Rule:

  • Often found using the Pythagorean Theorem:

(Slant Height)^2 = (Height)^2 + (Half of Base Length or Radius)^2
Represents the hypotenuse of a right triangle formed by the height and half the base (or radius).

Why this matters for the SAT:

Slant height is needed to calculate lateral surface area of pyramids and cones.
Recognizing it and using the Pythagorean Theorem prevents mistakes in geometry problems involving 3D shapes.