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.


a =  3.153 cm
R =  15.083 cm
o =  94.59 cm
S =  709.425 cm2


r=15 n=30 A=360/n=360/30=12 cosA/2=r/R R=r/cos(A/2)=15/cos(12/2)15.0826 (a/2)2=R2r2 x=R2r2=15.082621521.5766 a=2 x=2 1.57663.15313.153 cmr=15 \ \\ n=30 \ \\ A=360/n=360/30=12 \ \\ \cos A/2=r/R \ \\ R=r / \cos( A/2 )=15 / \cos( 12/2 ) \doteq 15.0826 \ \\ (a/2)^2=R^2 - r^2 \ \\ x=\sqrt{ R^2-r^2 }=\sqrt{ 15.0826^2-15^2 } \doteq 1.5766 \ \\ a=2 \cdot \ x=2 \cdot \ 1.5766 \doteq 3.1531 \doteq 3.153 \ \text{cm}
o=n a=30 3.1531=9459100=94.59 cmo=n \cdot \ a=30 \cdot \ 3.1531=\dfrac{ 9459 }{ 100 }=94.59 \ \text{cm}
S1=a r/2=3.1531 15/2=9459400=23.6475 S=n S1=30 23.6475=2837740=709.425 cm2S_{1}=a \cdot \ r / 2=3.1531 \cdot \ 15 / 2=\dfrac{ 9459 }{ 400 }=23.6475 \ \\ S=n \cdot \ S_{1}=30 \cdot \ 23.6475=\dfrac{ 28377 }{ 40 }=709.425 \ \text{cm}^2

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!

Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

Next similar math problems:

  1. Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  2. RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  3. Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
  4. Cathethus and the inscribed circle
    RightTriangleInradius In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
  5. Chord - TS v2
    chord_TS_1 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
  6. Inscribed rectangle
    rectangle_inside_circle What is the perimeter of a rectangle that is inscribed in a circle whose diameter is 5 dm long? Answer: 14 dm
  7. Equation of circle
    circle_analytics find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
  8. Circle - AG
    circle2 Find the coordinates of circle and its diameter if its equation is: ?
  9. Earth's circumference
    parallels Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
  10. The mast
    octagon A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
  11. Length IT
    lich2 Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c and the height h are given: a = 8 cm c = 2 cm h = 4 cm
  12. Perimeter of RT
    triangle_rt1 Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
  13. Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  14. Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  15. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  16. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  17. Isosceles triangle
    triangles_8 Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.