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What Are the Properties of Geometry?

Geometry is a subject that can be explored on various levels by elementary school students all the way through to graduate-level students. The properties of geometry comprise both basic and advanced material, but delving into specific properties such as shape, area, volume, measurement and the properties of circles presents an opportunity to gain an adequate understanding of geometry.
  1. Shape

    • A hexagon is a six-sided polygon.

      The most basic geometric property is shape. Shapes are determined by how many points, or vertices, they have, and the direction in X, Y and Z space those points occupy. If a shape has just one vertex, it is simply called a point. If it has two vertices, it is a line. If there are three or more vertices, the shape is a polygon if it is closed and all of its lines are straight. Traditional shapes are polygons: triangles, rectangles, squares, pentagons and so on.

    Length, Width, Height and Depth

    • The longest side of a rectangle is its length, while the shorter side is its width.

      When analyzing two-dimensional geometric shapes, only length and width are measured. If all sides are the same length, as in a square, then it doesn't matter which side is the length and which is width. However, if any one side is the longest in a shape, it should be the length. Three-dimensional objects also have length and width, but additionally possess either height or depth. Height and depth measure the same way, but height is for shapes that occupy space above "level," and depth is for shapes that occupy space below "level."

    Area and Volume

    • While squares have only area, objects like dice are squares that occupy three dimensions and possess volume.

      The size of a shape is comprised of a few individual properties. The width of an object is the space it occupies in X space: right to left. A shape's height is the space it occupies in Y space: up and down. And a shape's length is the space it occupies in Z space: forward and backward. Area is a calculation for two-dimensional objects that have only length and width. Area can be calculated by multiplying the length of a shape times its width. Volume, however, is used to measure the space inside of a three-dimensional object and is calculated by multiplying the length, width, and height of the shape.

    Circles

    • A round ball is a good example of a sphere, which is a three-dimensional circle.

      Because circles have no straight lines, they are not considered polygons. However, it is still possible to measure them. While you would measure the length of a polygon, you measure the circumference of a circle, which is the space around the circle, or the diameter, which is the length of a line that passes directly through the center of the circle. The radius of a circle is the length of a line that extends from the center of the circle to any part of the circle's edge. To calculate the area of a circle, multiply pi (3.14) times the length of the radius squared. A sphere is a circle that occupies three dimensions of space. To calculate the volume of a sphere, multiply 4/3 times pi (3.14) times the radius of the sphere squared.

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