# N-gon + area of shape - math 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. 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.
2. 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.
3. 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.
4. 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°.
5. Hexagon Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
6. 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?
7. 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.
8. 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.
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. 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?
14. Hexagon ABCDEF In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
15. 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!
16. 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
17. 30-gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
18. Center of gravity In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
19. Pentagon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
20. Glass How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?

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