# Polygon + right triangle - 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.

#### Number of problems found: 78

• 6 regular polygon It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm2 (square centimeters) has a circle in which is inscribed the 6-gon.
• 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.
• N-gon angles What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon?
• Find the Find the content of a regular 12 sided polygon, if its side a = 12 cm. Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• Regular n-gon Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?
• 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. .
• 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.
• 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.
• 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....
• 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?
• Five-gon Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
• Pentagon Calculate the area of a regular pentagon, which diagonal is u=17.
• Inner angles The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
• Hexagon Draw a regular hexagon inscribed in a circle with radius r=8 cm. What is its perimeter?
• Inscribed and described circle Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
• 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.
• Diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
• 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.
• Four sides of trapezoid Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.

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