# Polygon 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.

#### Number of problems found: 115

• Ferdinand
Ferdinand went from place A to place B and from there to place C. A is 7.2 km from B and B is 11.7 km from C. Albert went from place A to place D and from there to place C. D is 9.1 km from A and C is 10.8 km from D. Who traveled more and by how much?
• The perimeter 6
The perimeter of quadrilateral is 442.95 cm. If the three known sides measure 84.56 cm,132.77 cm, and 82.75 cm, how long is the fourth side?
• The coordinates
The coordinates (5, 2) and (-6, 2) are vertices of a hexagon. Explain how to find the length of the segment formed by these endpoints. How long is the segment?
• Polygon - area coordinates
Find the perimeter and the area of the polygon with the given vertices. T (2,7), U (2,9), V (5,9), W (5,7)
• Goat
The fenced flower bed has the shape of a regular hexagon. The tops are formed by fence posts. The fence around the flowerbed measures 60 m. A goat is tied to one of the pillars from the outside and grazes on the surrounding meadow (the goat should not ent
• Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.
• Hexaprism container
Calculate the volume and surface in the shape of a regular hexagonal prism with a height of 1.4 m with a base edge of 3dm and a corresponding height of 2.6 dm.
• Angles of a hexagon
Find the interior angles of a hexagon if the sizes of the angles form an arithmetic sequence, and the smallest angle is 70°.
• Pentagonal pyramid
Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm.
• Calculate
Calculate the surface of a regular eleven-sided prism; if the area of its base is 58 cm2, the edge of the base is 6cm long, the height of the prism is 21 cm.
• Ten persons
Ten persons, each person makes a hand to each person. How many hands were given?
• 9-gon pyramid
Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
• Octagonal prism vase
0.7 l of water can be poured in an octagonal prism vase. What is the height of the vase, if the bottom has a area of 25 cm square and a thickness of 12 mm?
• Hexagonal prism
Calculate the volume and surface of a regular hexagonal prism with the edge of the base a = 6 cm with the corresponding height v1 = 5.2cm and the height of the prism h = 1 dm.
• Find the
Find the content of a regular 12 sided polygon if its side a = 12 cm.
• Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
• Hexagonal pyramid
Calculate the volume and surface area of a regular hexagonal pyramid with a base edge a = 30 m and a side edge b = 50 m.
• Hexagonal pyramid
Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
• Which
Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm2 (B) 20 cm2 (C) 30.78 cm2 (D) 31.84 cm2 (E) 32.90 cm2