Polygon ProblemsExamples 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
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
- Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
We have a square with side 84 cm. We cut the corners to make his octagon. What will be the side of the octagon?
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
- Hexagon A
Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
- Angles of a hexagon
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
Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
- n-gon II
What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
- Each with each
Five pupils from 3A class played table tennis. How many matches did they play with each other?
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
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
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
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
Calculate the area of the regular pentagon with side 7 cm.
- Circle and hexagon
Calculate the radius of a circle whose circumference is 8.4 cm longer than the circumference of the inscribed regular hexagon.
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.
Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
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