Five-gon

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

Result

a =  7.053 cm
o =  35.265 cm
S =  85.593 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⋅ 6⋅ sin⁡(36∘)≐7.0534≐7.053 cmn=5 \ \\ R=6 \ \text{cm} \ \\ \ \\ Φ=360/(2 \cdot \ n)=360/(2 \cdot \ 5)=36 \ ^\circ \ \\ \ \\ \sin Φ=a/2 : R \ \\ \ \\ a=2 \cdot \ R \cdot \ \sin(Φ)=2 \cdot \ 6 \cdot \ \sin(36^\circ ) \doteq 7.0534 \doteq 7.053 \ \text{cm}
o=n⋅ a=5⋅ 7.0534=7053200=35.265 cmo=n \cdot \ a=5 \cdot \ 7.0534=\dfrac{ 7053 }{ 200 }=35.265 \ \text{cm}
h=R2−(a/2)2=62−(7.0534/2)2≐4.8543 cm  S1=a⋅ h2=7.0534⋅ 4.85432≐17.1185 cm2  S=n⋅ S1=5⋅ 17.1185≐85.5927≐85.593 cm2h=\sqrt{ R^2-(a/2)^2 }=\sqrt{ 6^2-(7.0534/2)^2 } \doteq 4.8543 \ \text{cm} \ \\ \ \\ S_{1}=\dfrac{ a \cdot \ h }{ 2 }=\dfrac{ 7.0534 \cdot \ 4.8543 }{ 2 } \doteq 17.1185 \ \text{cm}^2 \ \\ \ \\ S=n \cdot \ S_{1}=5 \cdot \ 17.1185 \doteq 85.5927 \doteq 85.593 \ \text{cm}^2

Try another example


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!
avatar




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

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. In a 2
    angles_7 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. .
  2. Rotatable tower
    veza Rotatable tower situated in the city center has ground shape of a regular polygon. If the tower is rotated by 14.4° around its centerpiece it looks from the side same. Your task is to calculate at least how many vertices can have a ground plan view of the.
  3. RT - inscribed circle
    rt_incircle In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
  4. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
  5. Clock face
    center_angle clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
  6. Centre of mass
    centre_g_triangle The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
  7. Vertices of RT
    RightTriangleMidpoint_3 Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
  8. Construct
    inscircle_triangle Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
  9. Chord
    chord_1 Point on the circle is the end point of diameter and end point of chord length of radius. What angle between chord and diameter?
  10. Inscribed triangle
    obluk To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
  11. Reference angle
    anglemeter Find the reference angle of each angle:
  12. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  13. Circles
    three-circles Three circles of radius 95 cm 78 cm and 64 cm is mutually tangent. What is the perimeter of the triangle whose vertices are centers of the circles?
  14. Annulus
    annulus_inscribed_circles 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.
  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. Line
    skew_lines It is true that the lines that do not intersect are parallel?
  17. Elimination method
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15