We will be working with regular
pyramids unless otherwise stated.
are three-dimensional closed surfaces.
The one base of the pyramid is a polygon and the lateral faces are
with a common vertex. The
vertex of a pyramid (the point, or apex) is not in the same plane as the
Pyramids are also called polyhedra
since their faces are polygons.
The most common pyramids are regular pyramids. A
regular pyramid has a regular polygon for a base and its height
meets the base at its center. The slant height is the
height (altitude) of each lateral face.
In a regular pyramid,
the lateral edges are congruent.
Since the base is a regular polygon, whose sides are all
congruent, we know that the lateral faces of a regular
pyramid are congruent isosceles triangles.
Pyramids are named for the shape of
volume of a
pyramid is one-third the product of the base area times the
height of the pyramid.
(Volume of a
B = base area, h = height)
= height (altitude) from vertex to base
B = area of base
The Great Pyramid of Egypt
The Great Pyramid of Khufu, at
Giza, Egypt, is 751 feet long on each side at the base, is 450
feet high, and is composed of approximately 2 million blocks of
stone, each weighing more than 2 tons. The maximum error
between side lengths is less than 0.1%.
The sloping angle of its sides
is 51°51'. Each side is oriented with the compass points
of north, south, east, and west. Each cross section of the
pyramid (parallel to the base) is a square.
Artist's rendering of the pyramids.
Until the 19th century, the
Great Pyramid at Giza was the tallest building in the world.
At over 4500 years in age, it is the only one of the famous
Seven Wonders of the Ancient World that remains standing.
According to the Greek
historian Herodotus, the Great Pyramid was built as a tomb for
the Pharaoh Khufu.