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Its vertical height is that of the perpendicular from the centre of the base to the apex; the slant height is the length of the sloping "corner" between two faces.

The height of a regular pyramid is the vertical distance from the center of base to the top and is usually shown with a line perpendicular to the base, denoted with a right angle to the base.

The slant height it the height of the lateral face (the triangles) from the edge of the base to the top of the pyramid. It is the height of the triangle, not the pyramid itself.

The slant height will also be the hypotenuse of a right angle formed from the altitude of the pyramid and the distance from the center of the base to the edge.

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Q: When you see a picture of a right pyramid with a regular polygon base how do you identify its height and its slant height?
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