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 Pre-algebra Arithmetics Integers Divisibility Decimals Fractions Exponents Percentages Proportional reasoning Radical expressions Graphs Algebra Monomials Polynomials Factoring Linear Equations Graphs of linear equations Rectangular Coordinate System Midpoint Formula Definition of Slope Positive and negative slope Determine the slope of a line Equations of lines Equation of lines (from graph) Applications of linear equations Inequalities Quadratic equations Graphs of quadratic equations Absolute Value Radical expressions Exponential equations Logarithmic equations System of equations Graphs and functions Plotting points and naming quadrants Interpreting Graphs Relations and Functions Function Notation Writing a Linear Equation from a Table Writing a Linear Equation to describe a Graph Direct Variation Indirect Variation Domain and range Sequences and series Matrices Inverse of a matrix Determinants Inner product Geometry Triangles Polygons 2-D Shapes 3-D Shapes Areas Volume Pythagorean Theorem Angles Building Blocks Geometry Transformations Parallel, coincident and intersepting lines Distances in the plane Lines in space Plane in space Angles in the space Distances in the space Similarity Precalculus Sequences and series Graphs Graphs Definition of slope Positive or negative slope Determine the slope of a line Equation of a line (slope-intercept form) Equation of a line (point slope form) Equation of a line from graph Domain and range Quadratic function Limits (approaches a constant) Limits (approaches infinity) Asymptotes Continuity and discontinuities Parallel, coincident and intersepting lines Introduction to Functions Limits Continuity Asymptotes Trigonometry Trigonometric ratios The reciprocal trigonometric ratios Trigonometric ratios of related angles Trigonometric identities Solving right angles Law of sines Law of cosines Domain of trigonometric functions Statistics Mean Median Mode Quartiles Deciles Percentiles Mean deviation Variance Standard Deviation Coefficient of variation Skewness kurtosis Frequency distribution Graphing statistics & Data Factorial Variations without repetition Variations with repetition Permutations without repetition Permutation with repetition Circular permutation Binomial coefficient Combinations without repetition Combinations with repetition

Areas
Regular polygon

A regular polygon is a polygon which is equiangular (all angles are congruent) and equilateral (all sides have the same length).

Attributes:

• The sides are the straight line segments that make up the polygon.
• The vertex is a corner of the polygon. In any polygon, the number of sides and vertices are always equal.
• The center is the point inside a regular polygon that is equidistant from each vertex.
• The apothem of a regular polygon is the line from the center to the midpoint of a side.
• The radius is the distance from the center to any vertex.
• By definition, all sides are the same length, so the perimeter is simply the length of a side times the number of sides.
 Area of a regular polygon: $Area=\frac{P\;\cdot\;a}{2}$ where P is the perimeter and a is the apothem Sometimes you will find a similar formula: $Area=\frac{s\;\cdot\;n\;\cdot\;a}{2}$ where n is the number of sides, s is the length of the each side and a is the apothem.

 Find the area of the regular polygon: $Area=\frac{P\cdot\;a}{2}$ = $\frac{40\;\cdot\;6}{2}$ = $\frac{240}{2}$ = 120 cm2

The lenght of the side of a pentagon is 10 units. The lenght of the apothem is 6.88. Find its area.

Area=