# 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. 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.
2. 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°.
3. 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.
4. Hexagon
Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
5. 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.
6. Each with each
Five pupils from 3A class played table tennis. How many matches did they play with each other?
7. 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.
8. The perimeter 2
The perimeter of the quadrilateral a = 1m b = 14/5m c = 2 3/10m d = 1 4/5m?
9. 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.
10. 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.
11. Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
12. Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
13. Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
14. The perimeter
The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
15. In a 2
In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
16. Six-sided polygon
In a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.
17. Diagonals
What x-gon has 54 diagonals?
18. Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
19. The mast
A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
20. Regular n-gon
In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.

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