Polygon Problems

Examples of a regular polygon (polygon). Polygon is a closed part of the plane bounded by a broken line. Points that define a polygon are the polygon vertices. The number of vertices, sides, and interior angles in a polygon is the same, and this number specifies the name of the polygon: triangle, quadrangle, pentagon, etc.

Number of problems found: 107

  • Diagonals in diamond
    diagonalsf In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
  • Sum of inner angles
    angle-sum-of-polygon Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
  • Pentagon
    5gon_1 Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
  • Hexagon
    hexa_prism Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
  • Octagon
    8gon We have a square with side 84 cm. We cut the corners to make his octagon. What will be the side of the octagon?
  • Decagon
    decanon Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
  • Hexagon A
    hexagon Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
  • Angles of a hexagon
    hexagon-irregular Find the interior angles of a hexagon if the sizes of the angles form an arithmetic sequence and the smallest angle is 70°.
  • Four sides of trapezoid
    lichobeznik2 Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
  • n-gon II
    x-gon_1 What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
  • n-gon
    x-gon What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
  • Each with each
    tenis_3 Five pupils from 3A class played table tennis. How many matches did they play with each other?
  • Diagonals
    diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
  • Hexagon ABCDEF
    hexagon_2 In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
  • Annulus
    annulus_inscribed_circles Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
  • Hexagon 5
    hexagon_1 The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon.
  • Regular 5-gon
    5gon_2 Calculate the area of the regular pentagon with side 7 cm.
  • Circle and hexagon
    circles_fun Calculate the radius of a circle whose circumference is 8.4 cm longer than the circumference of the inscribed regular hexagon.
  • Octahedron
    octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
  • Nine-gon
    9gon_1 Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.

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