Exploring regular polygons, this content delves into their defining features of equal sides and angles, and the importance of the apothem in symmetry and area calculations. It covers the area formula for regular polygons, utilizing trigonometry for determining unknown dimensions, and practical applications in calculating areas of shapes like squares and hexagons.
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Regular polygons have sides and angles that are all equal in length and measure
Equilateral Triangles
Equilateral triangles are regular polygons with three equal sides and angles
Squares
Squares are regular polygons with four equal sides and angles
Regular Pentagons
Regular pentagons are regular polygons with five equal sides and angles
Regular polygons have equal sides and angles, while irregular polygons have unequal sides and angles
The interior angles of a regular polygon can be calculated using the formula (n-2)×180°/n, where 'n' is the number of sides
The apothem is a line segment from the center of the polygon perpendicular to a side, used to establish symmetry and calculate area
The area of a regular polygon is given by the formula Area = (a×p)/2, where 'a' is the apothem and 'p' is the perimeter
The center of a regular polygon can be found by drawing bisectors of angles or connecting midpoints of opposite sides
Trigonometry can be used to find the apothem and side lengths of a regular polygon when they are not directly given
The principles of regular polygons can be applied to real-world scenarios, such as calculating the area of a hexagon or square
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Characteristics of regular polygons
Equal side lengths, equal angle measures, equilateral and equiangular.
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Minimum sides in a regular polygon
Three sides, as seen in an equilateral triangle.
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Difference between regular and irregular polygons
Regular polygons have all sides and angles equal; irregular polygons do not.
