Circle + polygon - practice problems
Number of problems found: 49
- Regular octagon pad
You need to make a pad in the shape of a regular octagon with a side length of 4 cm. What is the minimum diameter of the circle-shaped semi-finished product from which we make the pad, and what will be the percentage of waste? (Round the results to 1 deci - Difference 80618
A regular hexagon is described and inscribed in a circle. The difference between its areas is 8√3. Find the circle's radius. - Inscribed 43991
An irregular convex octagon is inscribed in the circle. Its four adjacent sides have a length of 3, and the remaining four adjacent sides have a size of 2. What is the area of a given octagon? - Dodecagon
Find the area of a regular dodecagon (n=12) if the radius of the circumscribed circle is 5 cm. - Circumscribed 7290
Calculate the area of a regular hexagon if the radius of the circle circumscribed is 6.8 cm. - Inscribed 7018
The dragon has the shape of a regular hexagon inscribed in a circle with a radius of 20 cm. What is the area of the dragon? - Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm - Circle and hexagon
Calculate the radius of a circle whose circumference is 8.4 cm longer than the inscribed regular hexagon's circumference. - 6-gon
The perimeter of a regular hexagon is 113. Calculate its circumradius (radius of a circumscribed circle). - Carousel for children
There are 5 seats evenly distributed on the children's carousel in the shape of a circle. What kind the arm of the carousel (connecting the center of the carousel to the seat) is long if the distance between with two seats is 1.2m? - Pentadecagon
Calculate the area of a regular 15-sides polygon inscribed in a circle with a radius r = 4. Express the result to two decimal places. - Pentagon
Calculate the length of a regular pentagon's side, circumference, and area, inscribed in a circle with a radius r = 6 cm. - 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. - The mast
A 40 m high mast is secured in half by eight ropes 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - 9-gon pyramid
Calculate a nine-sided pyramid's volume and surface, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm. - Nine-sided 36071
Calculate the surface area and volume of a regular nine-sided pyramid if the radius of the circle inscribed in the base measures ρ = 12 cm and the height of the pyramid is 24 cm - Circumscribed 22713
Calculate the circumference and the area of a regular ten-angle polygon if the radius of the circumscribed circle r = 20 cm. - 30-gon
At a regular 30-gon, the radius of the inscribed circle is 15cm. Find the side length a, circle radius R, circumference, and area. - Regular n-gon
Which regular polygon has a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm? - 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.
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