Five-gon

Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.

Correct result:

a =  7.0534 cm
o =  35.2671 cm
S =  85.5951 cm2

Solution:

n=5 R=6 cm  Φ=360/(2⋅ n)=360/(2⋅ 5)=36∘  sin⁡Φ=a/2:R  a=2⋅ R⋅ sin⁡Φ∘=2⋅ R⋅ sin⁡36∘ =2⋅ 6⋅ sin⁡36∘ =2⋅ 6⋅ 0.587785=7.053=7.0534 cm
o=n⋅ a=5⋅ 7.0534=35.2671 cm
h=R2−(a/2)2=62−(7.0534/2)2≐4.8541 cm  S1=a⋅ h2=7.0534⋅ 4.85412≐17.119 cm2  S=n⋅ S1=5⋅ 17.119=85.5951 cm2

Try another example


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
See also our trigonometric triangle calculator.
Pythagorean theorem is the base for the right triangle calculator.

You need to know the following knowledge to solve this word math problem:


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

Next similar math problems:

  • 6 regular polygon
    hexagon_2 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.
  • 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.
  • 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.
  • 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?
  • n-gon
    x-gon What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
  • n-gon II
    x-gon_1 What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
  • Regular 5-gon
    5gon_2 Calculate the area of the regular pentagon with side 7 cm.
  • Nine-gon
    9gon_1 Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
  • Hexagon area
    hexagon_1 The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area.
  • 9-gon pyramid
    9gon+Base+cone 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.
  • 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.
  • Decagon
    decanon Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
  • Hexagon
    hexa_prism Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
  • Hexagon A
    hexagon Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
  • Hexagonal pyramid
    hexa_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.
  • Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm
  • Glass mosaic
    6gon How many dm2 glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%.