# 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

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. - Pentagon

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

Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm. - Octagon

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

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? - n-gon

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? - 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

In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area. - Annulus

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. - 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

Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.

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