Nonagon

Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm

Correct answer:

S =  327.5732 cm²
o =  65.5146 cm

Step-by-step explanation:

$$\begin{gathered} r=10\text{ cm } \\ n=9 \\ A=360\mathrm{/}n=360\mathrm{/}9=40^{\circ } \\ \tan A\mathrm{/}2={\displaystyle \frac{a\mathrm{/}2}{r}} \\ a=2\cdot r\cdot \tan (A\mathrm{/}2)=2\cdot 10\cdot \tan (40\mathrm{/}2)\doteq 7.2794\text{ cm } \\ {S}_1={\displaystyle \frac{r\cdot a}{2}}={\displaystyle \frac{10\cdot 7.2794}{2}}\doteq 36.397{\text{cm}}^2 \\ S=n\cdot S_1=9\cdot 36.397=327.5732{\text{cm}}^2 \end{gathered}$$

$o=n\cdot a=9\cdot 7.2794=65.5146\text{ cm}$

Try another example

Showing 2 comments:

Math student

I need to draw a nonagon for my daughter and she has to have each at 4cm

1 year ago  Like

Matematik

try to start with angle 360/9 = 40°... Draw nine isosceles triangles with base a=4 cm and opposite angle 40°.
Or if you may calculate diameter of described circle - draw a circle and divide it into nine equal segments. (divide by 40° angle)

1 year ago  Like

Related math problems and questions:

• Pentagon
  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
  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.
• 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?
• Octagonal pyramid
  Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
• Perimeter of triangle
  In the triangle, ABC angle A is 60° angle B is 90°, and side size c is 15 cm. Calculate the triangle circumference.
• Pentadecagon
  Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• Nine-gon
  Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
• Calculate
  Calculate the area of triangle ABC, if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.
• Regular quadrangular pyramid
  How many square meters are needed to cover the tower the shape of a regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane are 68 °? Calculate coverage of waste by 10%.
• Decagon
  Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
• Tetrahedral pyramid
  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'.
• Hexagon in circle
  Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle.
• Pyramid 8
  Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
• Triangle SAS
  Calculate the triangle area and perimeter, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
• Diagonals of pentagon
  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.
• 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.
• Isosceles triangle 9
  Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle.