# N-gon + triangle - 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. 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....
7. Hexagon A
Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
8. 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.
9. n-gon II
What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
10. 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.
11. n-gon
What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
12. 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.
13. 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!
14. Nine-gon
Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
15. Hexagon
Draw a regular hexagon inscribed in a circle with radius r=8 cm. What is its perimeter?
16. Glass mosaic
How many dm2 glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%.
17. Children pool
The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film.
18. Hexagonal pyramid
Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
19. 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.
20. Diagonals
Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.

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