# N-gon - examples

Examples of a regular polygon (polygon). Polygon is a closed part of the plane bounded by a broken line. Points which 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.

1. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
2. Regular 5-gon Calculate area of the regular pentagon with side 7 cm.
3. Pentagon Calculate the area of regular pentagon, which diagonal is u=17.
4. Kites Boys run kite on a cable of 68 meters long. What is the kite altitude, if the angle from the horizontal plane is 72°?
5. Tower The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of sheet is required to cover the top of the tower if we count 8% of the sheet waste?
6. 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?
7. Hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
8. Hexagon A Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
9. Octahedron - sum On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
10. 4side pyramid Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees.
11. n-gon II What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
12. 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.
13. n-gon Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
14. n-gon What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
15. Hexagon - MO The picture shows the ABCD square, the EFGD square and the HIJD rectangle. Points J and G lie on the side CD and is true |DJ|
16. Hexagonal pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
17. Pentagonal pyramid Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
18. Hexagonal prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
19. Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
20. Hexagon Draw a regular hexagon inscribed in a circle with radius r=8 cm. What is its perimeter?

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