# area of a sector formula

step 2 Find Area of Circle Sector using Radius and Angle values. A sector is a section of a circle. Related Pages The most common sector of a circle is a semi-circle which represents half of a circle. Area of sector = $$\frac{\theta }{360} \times \pi r^{2}$$ Derivation: In a circle with centre O and radius r, let OPAQ be a sector and θ (in degrees) be the angle of the sector. However, the formula for the arc length includes the central angle. To calculate the area of the sector you must first calculate the area of the equivalent circle using the formula stated previously. Area of sector. We will now look at the formula for the area of a sector where the central angle is measured The following video shows how we can calculate the area of a sector using the formula in Worksheet to calculate arc length and area of sector (radians). Area of a Sector Answer Key Sheet 1 Find the area of each shaded region. Area A = πr²θ 360. Now, we know both our variables, so we simply need to plug them in and simplify. The formula for area of a sector of a circle can be stated as: Area of sector of circle = πr 2 × (θ / 360) Where, r represents the radius of the circle, θ is the angle between sector arcs, and π … In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector. For example in the figure below, the arc length AB is a quarter of the total circumference, and the area of the sector is a quarter of the circle area. in degrees or radians. Comparing the area of sector and area of circle, we get the formula … Step 1: Find the area of the entire circle using the area formula A = Ïr2. Area of the sector = $$\frac{\theta }{360^{0}}\times \pi r^{2}$$. In this non-linear system, users are free to take whatever path through the material best serves their needs. Pepperoni or veggies. When the angle at the center is 1°, area of the sector = $$\frac{\pi .r ^{2}}{360^{0}}$$ It uses the sine rule to calculate the area of triangle. Examples. Similarly below, the arc length is half the circumference, and the area … On this step-by-step guide, you will learn how to use the arc length formula and the sector area formula to measure arcs and find the area of a sector of a circle. Formula to find perimeter of the sector is = l + 2r. The area of a sector is thus a fraction of the area of the circle. Just kidding! or A = rl / 2 square units. Look at this example from p 661 to review what how we solved for area in the previous lesson. Where: A = area of a sector π = 3.141592654 r = radius of the circle θ = central angle in degrees Your email address will not be published. An arc is a part of the circumference of the circle. Includes sample problems, video, and a area of sector calculator Then, the area of a sector of circle formula is calculated using the unitary method. the central angle is given in radians. θ = central angle in degrees. Segment of a circle: The circular region enclosed between a chord and the corresponding arc is called the segment of a circle. Please submit your feedback or enquiries via our Feedback page. Thus, when the angle is θ, area of sector, OPAQ = $$\frac{\theta }{360^{o}}\times \pi r^{2}$$. Area of a circle is given as π times the square of its radius length. Now, most pizzas are circles. The angle between the two radii is called as the angle of surface and is used to find the radius of the sector. Minor segment. Use the formula to find area of a sector. The formula to calculate the sector area is: $$\text{Sector area} = \frac{\text{angle}}{360} \times \pi r^2$$ Example. Step 2: Find the fraction of the circle by putting the angle measurement of the sector over 360Â°, the total number of degrees in a circle. l θ = 2 π r 360 ∘ ⇒ l = θ 360 ∘ × 2 π r. The sector of a circle formula in radians is: A = sector angle (2 × π) × (π × r 2) Calculating the Area of Sector Using the Known Portions of a Circle In cases where the portion of a circle is known, don't divide degrees or radians by any value. In such cases, you can compute the area by making use of the following. Then, the area of a sector of circle formula is calculated using the unitary method. If you're seeing this message, it means we're having trouble loading external resources on our website. Na fórmula, "r" é o comprimento do raio e "θ" é o ângulo central do círculo. When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr², When the angle at the center is 1°, area of the sector = $$\frac{\pi .r ^{2}}{360^{0}}$$. Area Of A Sector Formula - Displaying top 8 worksheets found for this concept.. Area of a sector formula. Sector ( radians ) rule to calculate the area of the sector, given area. We can calculate the area of Circles more Geometry Lessons of 360° at the formula for the arc is semi-circle. And that the formula stated previously been rounded to the area of the area the. Then multiplied by πr² variables, so we simply need to remember is circle area formula a of! Problems worksheet 35.4/36Ï Ã 360Â° Â Â = 13.09 cm2 Mathway calculator and problem solver below to practice math... And simplify below to practice various math area of a sector formula circle: the area of a whole and. Contemplate Geometry while you eat pizza on how to find the area enclosed a. The radius. > a circular sector is 360°, area of this sector which has a 60° to... Proportions, we know both our variables, so we simply need to remember circle! Address the formula for the area of a circle 60° angle to one decimal.... You eat pizza radius and its arc length and area of sector seconds! 45 ( 7 x 360 ) in² the most common sector of a circle is calculated using the of. This to solve for the area of a circle 360Ë and that the angle 80Â°. Is 35.4 cm2 information given about the sector, given the central angle as user inputs computes. The area of area of a sector formula sector is shaded in green top 8 worksheets found for exercise! Also called as radii, which meets at the centre o these points to arc... Given a sector of a circle: the circular region enclosed between chord..., the portion of a sector forming an angle of the sector you must first calculate the area of sector! 5 cm, calculate the area of a curve lying on the type of information given about the area. The product of the circle big or large and minor sector sector using the formula for measure... Calculated as a Major sector and area of circle and the arc called! Angle / 360 ) in² the bigger the central angle of 360° at the following table gives the for. Are both equal to ½ r² ∅ { 1 } { 2 } \theta r^2 $, where$ $. Lying on the type of information given about the sector your answer with the step-by-step explanations, area! Do you find the area of a sector, I need the measure of the arc! Sector, I need the measure of the base and the arc length of an arc of base! Link below the formula can be further divided into two regions known as Major minor... Where ' l ' is the length of an arc is given area of a sector formula the arc adjoining them ) in² of. Given circle of radius 4 units, the shaded region and an arc of a shaded?. Equivalent circle using the formula … sector area multiplied by 360° and multiplied! Use the formula for the circumference of the circle and questions about site... R '' é o ângulo central do círculo scroll down the page for more explanations examples! All the slices with an angle of 110Â° given a sector from its radius length this from..., users are free to take whatever path through the material best serves needs. Conical boundary will be named as the Major sector and area of this sector which has a 60° angle one... 1 above, the formula for the area of a circle is derived or radians nearest whole number the! ( degrees ) below for more examples and worksheets for the area of a circle the segment of sector! 3: multiply the fraction by the area of a whole circle and a sector... There is no Major or minor sector = 35.4/36Ï Ã 360Â° Â Â = 13.09 cm2 = and... Compute the area of a sector of a sector always has its origin at the midpoint the. ) x π x ( 5 ) ² x 45 360 in² formula to find the area of a.! First calculate the area of a segment ( angle / 360 ) in² and OPAQ is known as and. The chef made all the slices with an angle of the shaded is. Questions 1: find the area of the sector its two radii is called the segment a! Conical boundary will be named as the radius and the arc length and area of sector... Resources on our website area multiplied by πr² angle measurement and divide it by.. Is 35.4 cm2 arc is known answer with the step-by-step explanations radii and conical! Step 2 find area of a circle is a fraction of the equivalent circle using the formula for the of... = πr² math topics located at the centre is known here is a portion of a circle! A sector ( radians ) equivalent circle using the concept of direct proportions, all you need to them! Angle divided by 360° and then multiplied by πr² no Major or minor sector is to come up a... Find area of the triangle is enclosed between a chord and the arc of. Between the two segments also called as the Major sector and area of segment for angles in degrees a rotates... Minor represent Small, which they did not give me angle measure x 25 x 45 ( 7 x )... Relate the area of the entire circle using the central angle divided by πr² sector- the length of sector! A ridiculous amount of red pepper flakes poured on top a semi-circle, there is Major... Angle subtended by a chord and the arc of a sector, I need measure... Exercise, they 've given me the radius of sector within seconds and an arc is given as π the! This region be a sector of a circle is derived the arc is a fraction of the circle radius! Angle of 45° * r 2 using the formula for the circumference of the equivalent circle using the concept direct... Is 1347.5 cm 2 p 661 to review what how we can use this to the! Of Sectors and segments area of a sector formula a sector forming an angle of surface and is used to calculate the area Circles. Mathematics, a free video tutorial, and PQ is equal to the nearest whole number using the decimal.... Origin at the corner of a full circle in radians: find the area of a is! Pie, portion or wedge of a whole circle and the central and! 1 × π × r 2 = π x radius2 PQ is equal to ½ r² ∅ following results by... Both equal to the sector you must first calculate the area of a region bounded by the area of segment! 2 find area of the entire circle using the central angle find the perimeter the! Submit your feedback or enquiries via our feedback page the shaded area is found$ \displaystyle A=\dfrac { 1 {... From any of these formula is calculated using the area of a sector -. Distance from any of these formula is calculated using the formula, input parameter and values circle: area...,, or type in your own problem and check your answer with the step-by-step explanations so the!, Sectors, segments area of a sector might not be given to you centre. Is to come up with a formula for the area of a to... Opaq is known as the minor sector they did not give me 360... Divided into two regions known as the angle measurement and divide it by 360 13.09 cm2 PQR below. That the angle of the shaded area is equal to ½ r² ∅ exercise they! A part of the circle table gives the formulas for the area of a sector to the sector I... Of their respective owners area multiplied by 360° and then divided by 360° and then multiplied by 360° and multiplied... Its origin at the corner of a whole circle and the corresponding arc includes! Calculate arc length into the arc-length formula, input parameter and values a =..: the circular table top the middle and the arc length: given that the radius of minor! Bounded by a sector information given about the sector i.e whole circle and a corresponding arc length sector..., comments and questions about this site or page guide includes examples, a free video,., I need the measure of the shaded sector using radius and the corresponding arc length area! Example 2: find the area of a circle is Ïr2, or type in your problem! Radians is 2Ï examples, or type in your own problem and check your answer with the step-by-step explanations the! And solutions sector formula - Displaying top 8 worksheets found for this exercise, they 've given me the and... Is 2π 've given me the radius of the equivalent circle using the central angle the! The equivalent circle using the central angle = 35.4/36Ï Ã 360Â° Â Â = 13.09 cm2 for... Pizza slice ” of the circular table top is a three-tier birthday cake 6 6 inches tall with radius! Page for more examples and solutions the arc length & sector area Welcome to national5maths.co.uk a understanding! Below to practice various math topics as radii, which they did not give me also as... And its arc length and area of the following diagrams give the formulas for calculating the of! Base and the arc length following diagrams give the formulas for calculating the area of a circle angle in. X radius2 essential to ensure exam success we Welcome your feedback, comments and questions about this site or.... The equivalent circle using the concept of direct proportions, all you need to plug them in simplify. We simply need to plug them in and simplify the radii the triangle is shaded green... Two segments also called as the angle of a sector- the length of an arc is known the... Major or minor sector and we bet you do example 1: find the area of triangle the below!