Regular Polygon

Regular Octagon Made By Cutting Equal Triangles Out From The Corners Of A Square

Problem
A regular octagon is made by cutting equal isosceles right triangles out from the corners of a square of sides 16 cm. What is the length of the sides of the octagon?

A.   6.627 cm C.   6.762 cm
B.   6.267 cm D.   6.276 cm

 

01 Maximum area of triangle of given perimeter

Problem 1
Show that the largest triangle of given perimeter is equilateral.
 

004-triangle-geven-perimeter.gif

 

10 Area common to three squares inside the regular hexagon

Problem
Three squares are drawn so that each will contain a side of regular hexagon as shown in the given figure. If the hexagon has a perimeter of 60 in., compute the area of the region common to the three squares. The required area is the shaded region in the figure.
 

Equilateral triangle bounded by three squares

 

Regular Pyramid

A regular pyramid is one whose base is a regular polygon whose center coincides with the foot of the perpendicular dropped from the vertex to the base.
 

The Regular Polygon

Rhombus is a quadrilateral with all sides equal (equilateral). Rectangle is a quadrilateral with all included angles are equal (equiangular). Square is both equilateral and equiangular, thus square is a regular polygon. Regular polygons are polygons with all sides equal and all included angles equal. Meaning, regular polygons are both equilateral and equiangular.
 

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