# N-gon - math word 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.

1. Five-gon Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
2. 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.
3. Top of the tower The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
4. Hexagonal pyramid Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. In a regular quadrilateral pyramid, the side edge is e = 7 dm and the diagonal of the base is 50 cm. Calculate the pyramid shell area.
6. Triangular pyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
7. Wall height Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
8. Hexa pyramid The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high.
9. Regular hexagonal pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture.
10. Octagonal pyramid Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
11. Hexagonal pyramid Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
12. Hexagon Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
13. Irregular pentagon A rectangle-shaped, 16 x 4 cm strip of paper is folded lengthwise so that the lower right corner is applied to the upper left corner. What area does the pentagon have?
14. Heptagonal pyramid A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 10 grams/cm3.
15. Each with each Five pupils from 3A class played table tennis. How many matches did they play with each other?
16. Octagonal tank The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness.
17. The perimeter 2 The perimeter of the quadrilateral a = 1m b = 14/5m c = 2 3/10m d = 1 4/5m?
18. MO Z8–I–6 2018 In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
19. Diagonals of pentagon Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
20. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm

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