Decagon

Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m

Correct result:

S =  2.9389 m2
o =  6.1803 m

Solution:

R=1 m n=10  A=360/n=360/10=36  sinA/2=a/2R  a=2 R sin(A/2)=2 1 sin(36/2)0.618 m  r=R2(a/2)2=12(0.618/2)20.9511 m  S1=r a2=0.9511 0.61820.2939 m2 S=n S1=10 0.2939=2.9389 m2
o=n a=10 0.618=6.1803 m



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
Do you want to convert length units?
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Pentagon
    5gon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
  • 30-gon
    30gon 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.
  • Diagonals of pentagon
    5gon_diagonal 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.
  • Pentadecagon
    220px-Regular_polygon_15_annotated.svg Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
  • Hexagon ABCDEF
    hexagon_2 In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
  • Tetrahedral pyramid
    ihlan Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
  • Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm
  • Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  • Arc and segment
    odsek_kruh Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 11 and corresponding angle is ?.
  • RT 11
    right_triangle Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
  • Hexagon A
    hexagon Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
  • Right triangle
    right_triangles Calculate the missing side b and interior angles, perimeter, and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
  • Hexagon in circle
    hexagon_3 Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle.
  • Regular n-gon
    regular_polygons Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?
  • Moon
    zem_mesic We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
  • Right angled triangle 3
    right_triangle_3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
  • Quadrilateral oblique prism
    kosyHranol What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35 ´ and the edges a, b form an angle of 50.5°.