Measures of Plane Figures and Geometric Solids
Chapter 2 Measures of Plane Figures and Geometric Solids Lesson 2. 1 Circumference Circumference is the linear distance around the outside of a closed curve or circular object. Dimension The dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Perimeter A perimeter is a path that surrounds an area. The word comes from the Greek peri(around) and meter (measure). The term may be used either for the path or its length – it can be thought of as the length of the outline of a shape Plane Figure Plane fgures are flat two-dimensional (2D) hape.
A plane fgure can be made of straight lines, curved lines, or both straight and curved lines. Lesson 2. 2 Area Area is a quantity that expresses the extent of a two-dimensional surface or shape, or planar lamina, in the plane. Area can be understood as the amount of material with a given thickness. Circular Region The set of all points of the plane which lie either on the circle or inside the circle form the circular region. The converse of the Pythagorean Theorem helps you to find out if a triangle is right.
Basically, the converse states that whenever the sum of the squares of two sides qual to the square of the third side of the triangle, the triangle is a right triangle. Diagonal Line The line Joining any two non-adJacent vertices of a polygon Graphing Paper Graph paper, graphing paper, or millimeter paper is writing paper that is printed with fine lines making up a regular grid. The lines are often used as guides for plotting mathematical functions or experimental data and drawing diagrams. Polygonal Region The union of the interior of a polygon with some, all, or none of the polygon itself.
Pythagorean Theorem In any right-angled triangle, the area of the square whose side is the hypotenuse (the ide opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs. Triangular Prism a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces Joining corresponding sides. Triangular Region A triangular region is the union of the triangle and its interior. Lesson 2. 3 Cube A cube is a three-dimensional solid object bounded by six square faces,facets or sides, with three meeting at each vertex.
The cube can also be called aregular hexahedron and is one of the five Platonic solids. Cylinder ne of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. a line segment Joining two adjacent vertices in a polygon. Thus applied, an edge is a connector for a one-dimensional line segment and two zero-dimensional objects. Faces Any of the individual surfaces of a solid object.
Lateral Edge The edges or the points which form the lateral faces of a solid figure are called the lateral edge. Lateral Faces The faces that Join the bases of a solid. Top of Form Lateral Surface he lateral surface of a solid is the face or surface of the solid on its sides. Length Length is the longest dimension of an object. In other contexts “length” is the measured dimension of an object. Oblique Cone A cone with an apex that is not aligned above the center of the base. Oblique Cylinder A cylinder with bases that are not aligned one directly above the other.
Oblique Prism A prism in which the bases are not aligned properly. Opposite Vertices Two vertices of a polygon with an even number of sides that have the same number of sides between them along either path around the polygon from one vertex to the other. Parallel Planes Planes that never intersect each other are known as Parallel Planes. Is a three-dimensional figure formed by six parallelograms. Polyhedron Polyhedron is a geometric solid in three dimensions with flat faces and straight edges.
Prism A prism is a polyhedron with an n-sided polygonal base, a translated copy (not in the same plane as the first), and n other faces (necessarily all parallelograms) Joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Pyramid A polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex forms a triangle. It is a conic solid with polygonal base. Rectangular Solid A rectangular solid is a 3 dimensional object with six sides, all of which are rectangles.
Right Cone Cone that has its apex aligned directly above the center of its base. The base need not be a circle. Right Prism A right prism is a prism in which the Joining edges and faces are perpendicular to the base faces. Right Rectangular Prism A solid (3-dimensional) object which has six faces that are rectangles. It is a prism because it has the same cross-section along a length. Right Triangular Pyramid A three-dimensional fgure with four triangular bases. Slant Height of a Cone The distance from the top of a cone, down the side to a point on the edge of the base.
The distance measured along a lateral face from the base to the apex along the “center” of the face. In other words, it is the altitude of the triangle comprising a lateral face solid The branch of geometry concerned with the properties of three-dimensional geometric fgures. Width The distance from side to side. Lesson 2. 4 Cavalieri’s Principle In geometry, Cavalieri’s principle, sometimes called the method of indivisibles, named after Bonaventura Cavalieri, is as follows: 2-dimensional case: Suppose two regions n a plane are included between two parallel lines in that plane.
Lateral Area Lateral surface area in a solid is the sum of the surface areas of all its faces excluding the base of the solid Volume Measure of solid content or capacity, usually expressed in units that are the cubes of linear units, such as cubic inches and cubic centimeters, or in units of dry and liquid measure, such as bushels, gallons, and liters. Eratosthenes of Cyrene As a Greek mathematician??eographer, poet, athlete,astronomer, and music theorist. He was the first person to use the word “geography” in Greek and he invented the iscipline of geography as we understand it. 3] He invented a system of latitude and longitude. Lesson 2. 5 Sphere Is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle, which is in two dimensions, a sphere is the set of points which are all the same distance r from a given point in space. Surface Area Mathematical description of the surface area is considerably more involved than the definition of arc length or polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces.