Area of pentagon inscribed in a circle

2. 44\text{ in }^2\) and the perimeter is 80 in. [6] In our example, area of triangle = ½ x 3 x 2 = 3 square units. If an n-sided regular polygon is inscribed in a circle of radius r, as shown in the figure below, then n-isosceles triangles fill the circle. Where “l” is the side length of polygon “n” is the number of sides of the polygon. Oct 19, 2023 · The area of a circle is A1 and the area of a regular pentagon inscribed in the circle is A2 . Determine the Central Angle: The central angle is crucial and is given by the formula: Central Angle \(= \frac{360^\circ}{n}\) Mar 18, 2019 · Our polygons we can divided into n n isosceles triangles. Find the area of a regular pentagon that is inscribed in a circle of radius 4cm. Prove that the area of the pentagon to be maximum, it must be a regular one. Practice 2 - Construct a regular pentagon that will fit in the circle below. 19 feet and the area is approximately 81516. 9. Probably α1 10. 3 days ago · Our octagon area calculator is capable of finding the radii of the circumscribed and inscribed circles. 49 square feet. (1) proves it is a parallelogram, (2) that it is a rectangle, and (3) that it is a rhombus. increased, the area of the figure got closer to π. ϕ ( − π 5 ≤ ϕ ≤ π 5) . Probably α1 The area of the circle and the area of a regular polygon inscribed the circle of n sides and of perimeter equal to that of the circle are in the ratio of. A regular pentagon is inscribed in a circle with centre O, of radius 5 cm, as shown below. Step 4: Construct the perpendicular bisector of line segment OC O C. 3 Calculate the total area of the pentagon. ⁡. Now, if a regular hexagon is inscribed in a circle then its side is equal to the radius of circle. --. Answer: We know that the triangle inscribed by a chord that passes through the centre of the circle is a right triangle. It has an interesting relationship with the formula for the circumference of a circle, which is 2 * Pi * R (and that is a consequence of the definition of Pi, which is defined to be the ratio of the circumference Mar 4, 2018 · $\begingroup$ One way of thinking about an integral is that you want to divide up the area/volume etc which is your target into bits which are easy to compute (without leaving too much gap or allowing too much overlap). What is the area of the shaded part of the circle? A circle is inscribed in a regular pentagon whose sides are 12 cm. Step These form the diagonals of your quadrilateral. Answered 2 years ago. Thus it is proven to be a square. A regular hexagon is polygon whose all sides are equal and it has been made of six equilateral triangle. The sum of the lengths of all diagonals of is equal to , where and are relatively prime positive integers. So if you want a circle touching a specific corner of your polygon, that becomes very cheap now. Nov 14, 2020 · Given that the inscribed polygon is regular, we can say that the angle subtended between any 2 line segments (originating from adjacent corners) at the center of the circle will be equal and since there will be n n unique angles totaling up to 2π 2 π, each of them will be equal to 2π n 2 π n. 14 15 23 31 A square of perimeter Step 1: Use the given diagram and properties of polygons, tangents, and inscribed circles to determine which segments of the polygon are congruent, and identify the lengths of these segments. 5. Find the area inside the pentagon and outside the circle. Use the Polar Moment of Inertia Equation for a triangle about the. Hypotenuse theorem can be applied here, The diameter of the Sep 14, 2023 · The video explains how to solve a Multiple Choice Question on Areas related to circles chapter in an easy way. Jun 15, 2022 · The area of a regular pentagon is \(440. Construct the perpendicular diameter (i. Jul 16, 2022 · Product of regular n-gon diagonals inscribed in unit circle = n 7 No polygon has the same area as the difference between its inscribed and circumscribed circles Inscribed Shapes. Actually, this is quite simple. " When a circle is inscribed inside a polygon, the edges of the polygon are tangent to the circle. Thus, area of the circular window, Area = πr 2. Therefore, area of the inscribed circle is 154 square in. What is the perimeter of a regular hexagon circumscribed about a circle of radius 1? A circle is inscribed in a regular pentagon. Algebra. Moment of Inertia. In Figure 2. The area is 1/2 base times altitude of the triangle that consists of one of the pentagon's sides and the radii to the two endpoints of that side. Oct 23, 2007 · Re: A regular pentagon is inscribed in a circle. Here: r is the radius; c is the chord's length; and. S k K L a N 5 A B C M = D E O T Figure 4. Set the compasses on M and adjust its width to N. Exercises 1. Using the same method as for the pentagons, we get: Area of smaller polygon = 1/2 x n x sin (360/n) Area of larger polygon = n x tan (360/2n) where n is the number of sides of the polygon. Topic: Circle. Interact with this applet to get familiar with the concepts. ( x1, y1) axes where: Multiply this moment of inertia by n. You can always think of area as the number of squares required to completely fill in the shape. Using the given radius, the side length is approximately 688. Consider the following diagram of the 5-pointed star: Clearly the area of the 5-star is 10 times the area of the orange-shaded triangle OAP which, in turn, equals half the height times the base: A( OAP) = 1 2 ¯ AC ⋅ ¯ OP = 1 2 ¯ AC ⋅ r To find ¯ AC notice that it is a joint side of two right triangles, OAC and PAC, hence ¯ OC Here’s the best way to solve it. If I n is the area of n sided regular polygon inscribed in a circle of unit radius and O n be the area of the polygon circumscribing the given circle, prove that I n = O n 2 (1 + √ 1 − (2 I n n) 2) Let A, be the area of a polygon with n equal sides inscribed in a circle with radius r. If you divide the pentagon into congruent triangles, you can quickly find the area of the shape. 1(b), \(\angle\,A\) is an inscribed angle that intercepts the arc \(\overparen{BC} \). Figure 6. Find the area of the circle. The perimeter of the pentagon is 150 cm. (It is a polygon in a circle) A circumscribed polygon is a polygon in which each side is a tangent to a circle. To find the total area, just multiply the area of one triangle by five. A pencil for drawing and annotations. Area of Regular Polygon Inscribed in a Circle. Mar 1, 2024 · Regular octagon calculator. Mar 10, 2023 · For $\lambda=0$ you get the point itself, as a circle of radius zero. The symmetry can be seen by regarding the polygon as the union of isosceles triangles Dec 18, 2017 · A pentagon is inscribed inside a circle. 6 on page 42 . So, Area of incribed circle = π( a 2 tan π n)2 Area of incribed circle = π ( a 2 tan π n) 2. a regular pentagon has 5 equal sides, the circle inscribed in the pentagon touches at each of the midpoints of these 5 sides, perimeter of the pentagon is 150 cm, 150/5 = 30 so each side of the pentagon is 30 cm, May 6, 2021 · Question: Triangle ΔABC is inscribed in a circle O, and side AC passes through the circle’s centre. Find the Area of HexagonFind the Area of PentagonFind the area of the region inside the pentagon but outside the hexagon. While the pentagon and hexagon formulas are complicated, we show that each can be written in a surprisingly compact form related to the formula for the discriminant of a cubic polynomial in one variable. Sep 16, 2022 · Figure 2. Question. For $\lim_{\lambda\to\pm\infty}$ the equation approaches the line, as a circle of infinite radius. You can obtain 2 * a/2 directly from the two right triangles formed by taking the radii at two edges on the Nonagon and splitting that triangle in half, using basic Trigonometry. Find the circle’s diameter. circle with center Oand radius jOSjand denote the point where this circle crosses the line segment ONby T. 2: Circles The circle is one of the most frequently encountered geometric figures. 1: (left) inscribed circle (right) inscribed circle with radius. Radius of circle = 14/2 = 7 in. Jul 18, 2022 · The area of a polygon is the amount of two-dimensional space inside the polygon, and it is measured in square units: square feet, square centimeters, square miles, etc. Circle Inscribed polygon Based on the statement and figure above answer the following: 1. Express the area of the isosceles Created by user's request. Solution For *14. Verified. Since it's inside a pentagon like this, it's called an inscribed figure. Draw a broad arc that crosses the given circle in two places. The area of one of these triangles is 1/2*base*height = 1/2*r*r*sin(2π/n). Intersections A;Bof the latter circle and the circle kare the endpoints of the side of a regular pentagon inscribed in k. There’s a nice way to see why the formula for the area of a circle of radius R is: Pi * R 2. As the number of sides n gets larger and larger, it is easy to see that ‘ !r and P !C; the circumference of the circle. Q14 - A regular pentagon is inscribed in a circ Mar 18, 2019 · Our polygons we can divided into n n isosceles triangles. 10. Inscribed Polygon. OAB = 108/2 = 54. 2k points) If I n is the area of n sided regular polygon inscribed in a circle of unit radius and O n be the area of the polygon circumscribing the given circle, prove that I n = O n 2 (1 + √ 1 − (2 I n n) 2) Jan 11, 2024 · Explore Tutors by Cities. Apr 10, 2024 · To find the area of any triangle, just calculate ½ x base x height. Mar 25, 2016 · If we draw an altitude from the vertex angle to the base of an isosceles triangle, it bisects both the vertex angle and the base, as shown in the Figure below. Similar to my perimeter findings, when the number of sides of the regular polygon. Regular polygons are equilateral (all sides equal) and also have all angles equal. An = 1/2nr^2 sin (2pi/n)This answer has not been graded yet. 4 . The area of a quadrilateral inscribed in a circle is given by Bret Schneider’s formula as: May 15, 2024 · An incircle is an inscribed circle of a polygon, i. Math Open Reference Area. 14 15 23 31 A square of perimeter Dec 1, 1994 · In this paper we derive formulas giving the areas of a pentagon or hexagon inscribed in a circle in terms of their side lengths. Since. The tool can calculate the properties of the octagon, given either the length of its sides, or the inradius or the circumradius or the area or the height or the It's a circle. Was this answer helpful? A square is inscribed in a circle or a polygon if its four vertices lie on the circumference of the circle or on the sides of the polygon. Let R be the radius of the circle circumscribing n-sided polygon. Find the length of the apothem of the pentagon. Aug 3, 2023 · An inscribed polygon is a polygon that has all its vertices on a circle. Label them A and E. In this case, since all interior angles are equal, each interior angle = 108˚. Using. \text {Total Area}=15+50=65 Total Area = 15 +50 = 65. (3) They are perpendicular, per construction. Jan 11, 2024 · This video creates a formula and strategy to find the area of ANY regular polygon inscribed in a circle with a given radius r. Label the point where the bisector intersects the line segment with a P P. Since C = 2ˇr, the area of the regular inscribed n-gon gets closer and closer to 1 2 r 2ˇr Hi there. This tool calculates the basic geometric properties of a regular octagon. All regular polygons starting from an equilateral triangle, a square, a pentagon, or a hexagon Jul 18, 2022 · Figure 1. Step 5: Open your compasses to a radius that matches the distance from point O O to point P P. These trangles have surface area: So polygons have surface area: That's why: Moreover: α1 +α2+ +αn = 2π α 1 + α 2 + + α n = 2 π. An incircle of a polygon is the two-dimensional case of an insphere of a solid. , inscribed in a circle) then the area of the polygon is uniquely determined. Many geometry problems deal with shapes inside other shapes. (a) Let An be the area of a polygon with n equal sides inscribed in a circle with radius r . Consider supporting lines x cos ϕ + y sin ϕ = f(ϕ) x cos. The area of a regular octagon is \(695. Your answer is correct and θ = 2π n θ = 2 π Jun 18, 2017 · This altitude height will also be the radius of the circle inscribed in it. Find the area of the Hexagon. Step 6: Using your straight edge, draw a line One possible method (though there's a few ways to do it) is: 1. The Apothem (the dashed line in the applet below) is the length from the center of the regular to one of its sides. Can you help her calculate the area of the inscribed circle? Solution: Each side of the square curtain = 14 in. (a) Let An be the area of a polygon with n equal sides inscribed in a circle with radius r. Initiate with a Circle: Begin by drawing a circle of the desired radius using the compass. Figure B shows a square inscribed in a triangle. Where A₀ means the area of each of the equilateral triangles in which we have divided the hexagon. For inscribed quadrilaterals in particular, the opposite angles will always be supplementary. 1 6. Find the radius of the circle? A regular Math. Then A1 : A2 is asked Jun 26, 2019 in Mathematics by Shilpy ( 64. And the area of AOB = 1/2 AOsin angle AOB. Label them B and D. the perpendicular bisector of the first diameter). The pentagon could be inscribed in a circle with radius of 300 feet. The inscribed circle will touch each of the three sides of the triangle at exactly one point. r is the radius of the circle in which the polygon is inscribed. s 2 = r sin(θ) s 2 = r sin. Procedure: 1. then angle AOB = 360/5 = 72 degrees. and a regular hexagon inscribed in that circle. For an arc measuring θ°, the arc length s, is s= 2*π*r*θ°/360°. Find the area of the courtyard. It is the point where the angle bisectors the polygon or its area. I have read When is the area of a pentagon inscribed inside a fixed circle maximum?, but am not satisfied with the answer My approach: We can divide the pentagon into a triangle and a cyclic quadrilateral by joining any two May 1, 2024 · Since the polygon is inscribed in the circle, of special interest are the inscribed angles, which are the vertices of the polygon that lay on the circle's circumference. 3. a regular pentagon has 5 equal sides, the circle inscribed in the pentagon touches at each of the midpoints of these 5 sides, perimeter of the pentagon is 150 cm, 150/5 = 30 so each side of the pentagon is 30 cm, Oct 22, 2023 · A compass for drawing the circle and aiding in polygon construction. Perimeter of incribed circle = 2π( a 2 tan π n) Perimeter of incribed circle = 2 π ( a 2 tan π n) Area of polygon = n ⋅ 1 2a( a 2 tan π n) Area of polygon = n ⋅ 1 2 Nov 28, 2020 · An inscribed polygon is a polygon where every vertex is on the circle, as shown below. Since there are n such identical . Draw a line from A to B, then B to C etc, until you have drawn all five sides of the pentagon. Hence, the perimeter of regular hexagon = 6r. The product of the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the product of its two pairs of opposite sides. Express h and the base b of the isosceles triangle shown in terms of and r. Our user asked us to create a calculator which should determine the "side length of the regular polygon (pentagon, hexagon) by diameter or radius of a circumscribed circle". An inscribed figure is a shape drawn inside another figure. Area of a Circle or Regular Polygon. You can notice that the circumradius is simply half of the length of the longest diagonal: R = l/2 = a / 2 * √(4 + 2√2) Similarly, the inradius is the same as the apothem, which is just half of the octagon's height: Dec 15, 2023 · We can generalise the method we used to find the pentagon areas to enable us to quickly calculate the inner and outer polygons for any number of sides. Draw the circle with center Nand radius jTNj. Upvote • 1 Downvote. We want to know. Solution. Dec 31, 2020 · A regular polygon is a polygon in which all sides are equal and all angles are equal, Examples of a regular polygon are the equilateral triangle (3 sides), the square (4 sides), the regular pentagon (5 sides), and the regular hexagon (6 sides). n is the number of sides. 1 Types of angles in a circle. Then f f periodic with period 2π 5 2 π 5, and one has. Nov 8, 2016 · $\lim_{r\to\frac12} A(r) =0$ and $\lim_{r\to 1} A(r) =\pi$. 3\text{ cm }^2\) and the sides are 12 cm. The area of a regular polygon inscribed in a circle formula is given by: inscribed inside a circle of radius r: A = 1 2 ‘P; where ‘ is the length of an apothem and P is the perimeter of the polygon. May 25, 2021 · Final answer: To find the area of the courtyard, you can use the formulas for finding the side length and area of a regular pentagon inscribed in a circle. [Hint: Use Equation 1. Area = 22/7 × (7) 2. Find k ∗ h? View Solution Q 5 Jul 19, 2020 · The area of a regular Nonagon can be calculated using the basic formula A = 9/4 * a^2 * cot (20°), where a represents the length of one side. Area of a Regular Polygon (with a radius drawn to the center of one side) [3] For a regular polygon with n n sides of length s s, and inscribed (inner) radius r r, A = nsr ÷ 2 A = n s r ÷ 2. Aug 3, 2023 · In geometry, an inscribed circle, also known as the incircle of a polygon is the largest possible circle that can be drawn inside a regular, cyclic polygon. cos (π n): π n; tan (π n): π n; sin (π n): π n; cot (π n): π n How to find area of shaded region involving polygons and circles, Find the Area of a Circle With Omitted Inscribed Triangle, Find the area of a shaded region between and inscribed circle and a square, Find the area of a shaded region between a square inscribed in a circle, How to Find the Area of a Rectangle within Another Rectangle, Grade 7 in video lessons with examples and step-by-step A square is inscribed in a circle or a polygon if its four vertices lie on the circumference of the circle or on the sides of the polygon. Let such a pentagon have edge lengths , , , and area , and let (1) Jun 3, 2013 · It is easier to start with a regular pentagon with vertices on the unit circle, one of them at (1, 0) ( 1, 0), and finding the smallest square containing it. Enter a number of sides (from 3 to 360), use the slider, or use the next and prev buttons to inscribe a regular polygon in the circle of radius 7 provided. Two-dimensional figure measured in terms of radius. d is the chord's distance to the circle's center. The center I of the incircle is called the incenter, and the radius r of the circle is called the inradius. Third construction 3 days ago · Write down the chord length formula: c = 2 · √(r² - d²). Perimeter. (a) By dividing the polygon into n congruent triangles with central angle 21 n show that 211 An = nas sin Consider the following diagram examining one of the n congruent triangles. However I don't know how to use S′(α) S ′ ( α) to find polygons with largest area because I have sum of n n other cos cos. Area of Regular Polygon Formula = [l 2 n]/[4tan(180/n)] Square units. Now, each of these triangles is an isosceles triangle, made up of two radii r of the inscribed circle, and an angle 2π/n at the center of the circle. Area = 154. The most popular, and usually the most useful formula is the one that uses the number of sides n n and the side length a a: A = n \times a^2 \times \frac {1} {4}\cot\left (\frac {\pi} {n}\right) A = n × a2 × 41 cot(nπ) However, given other parameters, you can also find out the area: – incircle radius (it If the area of the circle is A 1 and the area of the regular pentagon inscribed in the circle is A 2 then the ratio A 1 ∣ A 2 be π k sec (π h). Bisect one of the right angles, and draw another diameter - that gives you four arcs subtended by 45°, two on each side of the circle. cos (π n): π n; tan (π n): π n; sin (π n): π n; cot (π n): π n Apr 10, 2019 · Learn how to find the area of a regular polygon when only given the radius of the the polygon. 23. 4. This is the Polar Moment of Inertia of a Regular n sided Polygon about the Centroidal Axis. An inscribed polygon is a polygon in which all vertices lie on a circle. We've divided the pentagon into five equal triangles. That circle is inscribed in a Pentagon. The result will be the length of any chord at that distance from the circle's center. The circle is inscribed in the polygon and the polygon is circumscribed Find the area (in sq. Verified by Toppr. Inscribed Quadrilateral Theorem: A quadrilateral can be inscribed in a circle if and only if the opposite angles are supplementary. 15. Draw a radius from the center of the circle to each corner of the pentagon. 11. Multiply by five to find the total area. (1) They bisect each other, because they cross at the center. There are (5 – 2) x 180˚ = 540˚ in any pentagon. Also B n is the area inside the polygon and outside the circle inscribed in the polygon. We say that the circle is inscribed in the pentagon. Also, check: Area of Regular Polygon Calculator. 4 Write the answer, including the correct units. Area of circle = πr 2. The perimeter of a regular polygon with n n sides of side length s s is P = ns P = n s. = a × √3/2 × a / 2. Figure C shows a square inscribed in a quadrilateral. cot is the cotangent function. The largest pentagon that will fit in the circle, with each vertex touching the circle. A regular hexagon with a perimeter of 24 units is inscribed in a circle. If n = 4 then B n is equal to A = bh = 10× 5 = 50. , a circle that is tangent to each of the polygon's sides. However, if we impose the condition that the polygon be convex and cyclic, (i. 1 1. 19. This equation is a reminder that the area of a unit circle will be equal to π. Replace r and d with their respective values. The perimeter of a regular polygon with \(n\) sides that is inscribed in a circle of radius \(r\) is \(2nr\sin\left(\frac{\pi}{n}\right). The former represents almost perfectly retracing the first side along a very short arc that is almost a straight line; the latter represents going around the circle in what is almost a regular inscribed polygon. ϕ = f ( ϕ). \) Using similar methods, one can determine the perimeter of a regular polygon circumscribed about a circle of radius 1. Question from Victoria, a student: find the area of a regular pentagon inscribed in a circle with radius 3 units Here’s how you can determine the angles in the diagram. 12r. What is the length of the apothem? A regular 20-gon and a regular 40-gon are inscribed in a circle with a radius of 15 units. The polygon is inscribed in the circle and the circle is circumscribed about the polygon. inscribed and circumscribed polygons, I found the area of each shape and compared these values to π. Practice 3 - Draw the largest possible circle inscribed in this equilateral triangle. Given a circle with radius 2 ft. The total area of the pentagon is found by adding the area of the triangle and the area of the rectangle together. We go through an example involving a regular pentagon inscrib A circle is inscribed in a regular pentagon. While an incircle does not necessarily exist for arbitrary polygons, it exists and is moreover Question 3904: area of a regular pentagon inscribed in a circle of radius 12cm. May 1, 2024 · Since the polygon is inscribed in the circle, of special interest are the inscribed angles, which are the vertices of the polygon that lay on the circle's circumference. = √3/4 × a². The center of such a circle is called the incenter. An inscribed angle of a circle is an angle whose vertex is a point \(A\) on the circle and whose sides are line segments (called chords) from \(A\) to two other points on the circle. Given a circle with a radius of 2 ft. By dividing the polygon into n congruent triangles with central angle 2pi/n, show that the following is true. The formula for calculating the area (A) of an inscribed polygon with n sides is given by: A = (1/4) * n * r^2 * cot (180°/n) where: n is the number of sides of the polygon. Moreover, it is a symmetric function of the side lengths. (2) They are congruent, since they are both diameters. And in between you have all the circles touching the line in that point. In doing this activity, we will lear 1 day ago · Using this, we can start with the maths: A₀ = a × h / 2. GEOMETRY Find the area of a regular pentagon inscribed in a circle whose equation is given by (x-4) + (y + 2)² Mar 30, 2020 · In this GeoGebra tutorial, we will learn how to approximate the area of a circle by inscribing a polygon using GeoGebra. After multiplying this area by six (because we have 6 triangles), we get the hexagon area formula: A = 6 × A₀ = 6 × √3/4 × a². 1. 7. With the tip of your compasses on point P P, draw a circle. e. If A and B are [ #permalink ] Fri Jul 19, 2013 7:56 am. You multiply that area by 5 for the area of the pentagon. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. We have to find the length of the base of the triangle, which is formed by the center of the polygon and two 3 days ago · Area of a regular polygon formulas. How to construct (draw) a regular pentagon inscribed in a circle. The area of the circle and the area of a regular polygon inscribed the circle of n sides and of perimeter equal to that of the circle are in the ratio of. By dividing the polygon into n congruent triangles with central angle 2 π / n, show that An=(1)/(2) n r^2sin((2 π)/(n)) (b) Show that limn →∞ An=π r^2 . The perpendicular bisectors of the four sides of the inscribed quadrilateral intersect at the center O. These radii divide the pentagon into five isosceles triangles each with a center angle of 360/5 = 72 degrees (once around the circle, divided by five triangles Let be a pentagon inscribed in a circle such that , , and . Any central angle formed by connecting adjacent vertices of the pentagon to the center of the circle must be 1/5 of 360˚ = 72˚. Given, BC = 16 and AB = 12. 4 days ago · A cyclic pentagon is a not necessarily regular pentagon on whose polygon vertices a circle may be circumscribed. O na A B с i The diagram shows one of the n congruent triangles, AAOB, with Sep 27, 2023 · The base of each triangle has length equal to the side length of the polygon. The center of the Pentagon in Arlington, Virginia, is a courtyard in the shape of a regular pentagon. The sum of interior angles of n sides : (n-2)*180 , here its 540. (b) Show that lim n right arrow infinity An = ppir^2. For example, circles within triangles or squares within circles. Any polygon inscribed in a circle is Regular polygon implies all the angles are equal , hence each angle is 540/5 = 108. Answer by khwang (438) ( Show Source ): You can put this solution on YOUR website! Let AB be a side of the pentagon and O be the center. The inner shape is called "inscribed," and the outer shape is called "circumscribed. It is also known as ‘polygon in a circle’, as the polygon is found inscribed in a circle and the circle is found to be circumscribed around the polygon. Figure A shows a square inscribed in a circle. cm) of a regular octagon inscribed in a circle of radius 10 cm? Pinoybix area of a regular octagon problems with solutions. Construct a diameter. We know that we can compute the length of the arc from the central angle that subtends the same arc. Let A n be the area that is outside a n-sided regular polygon and inside it's circumscribing circle. ex om pq ou qr sf pd sk da ko