Base (in Geometry)

Elementary School

Definition

Base is a term used in both plane geometry and solid geometry. A base can refer to the surface a 3-dimensional object that sits on or the bottom side of a shape. If the top is parallel to or the same as the bottom, both the top and bottom are called bases.

Worked examples

\(\)Area of triangle\( = \frac{1}{2} \times \)base\( \times \)height\(\)

In a triangle, any side can be the base; height is perpendicular to that base.

\(\)Volume of cylinder\( = \pi r^2 h\)

The base is the circular surface the cylinder sits on; \(\pi r^2\) is its area.

\(\)A prism has two parallel congruent bases\(\)

Both the top and bottom faces are bases because they are parallel and identical.

Common mistakes

Calling the longest side of a triangle the base → Any side can be chosen as the base The base is whichever side you measure height perpendicular to; it's a choice, not fixed by length.
Thinking only the bottom surface is the base in a prism → Both top and bottom parallel faces are bases When top and bottom are congruent and parallel, both are called bases by definition.
Confusing base with the slant height in pyramids → Base is the polygon the pyramid sits on, not a slanted edge The base is the flat polygon at the bottom; slant height is measured along a face.

Where you'll use it next

You'll use base to calculate areas of triangles and parallelograms, volumes and surface areas of prisms, cylinders, pyramids, and cones, and to identify corresponding parts in congruent and similar figures.

Found in 1 StudyPug lesson

Triangle Area and Perimeter: Mastering Fundamental Geometry

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Unlock the power of triangle geometry! Learn to calculate area and perimeter with confidence. Perfect for students seeking to enhance their math skills and tackle real-world problems.

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