how to find area of a sector

This area is equivalent to the median angle. Examples. You can find it by using proportions, all you need to remember is circle area formula (and we bet you do! What is a Variable? Whenever you want to find area of a sector of a circle (a portion of the area), you will use the sector area formula: Now that you know the formulas and what they are used for, let’s work through some example problems! This free area calculator determines the area of a number of common shapes using both metric units and US customary units of length, including rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram. With these measurements finding the area of a sector is a simple matter of plugging the numbers into given formulas. Using Radius to Find Area Identify the radius of a circle. For a more detailed explanation, please click on the attached Arc Lengths & Sector Areas Theory Guide in a Nutshell. In order to find the area of this piece, you need to know the length of the circle's radius. Loading... Save for later. It’s a percent or portion of a disk that is enclosed by that arc and two equal radii. The total area of a circle is πR 2 corresponding to an angle of 2π radians for the full circle. Note: A circular sector or circle sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. Subscribe to our channel for free! That gives you the circumference. Examples. Now that you know the formulas and what they are used for, let’s work through some example problems! Here’s the formal solution: Find the area of circle segment IK. Next, take the radius, or length of one of the lines, square it, and multiply it by 3.14. Divide the central angle by 360. Free. Through an example question, we'll demonstrate how the relationship between the area of a section and total area can help you find the section's area. Double the radius, then multiply by pi. In simple terms it looks like a slice of pie. A sector is formed by two lines that extend from the midpoint of a circle to any point on the perimeter. Related Topics. Then check out this tutorial! Our area of a sector calculator is flexible and reliable. To find the area of the sector, I need the measure of the central angle, which they did not give me. We use cookies to make wikiHow great. Multiply that fraction by 360°. Therefore, to get the area of this slice of pizza, you will need to find the area of the circle and then divide the result by 4. the whole circle = πr^2 Whenever you want to find the length of an arc of a circle (a portion of the circumference), you will use the arc length formula: Where θ equals the measure of the central angle that intercepts the arc and r equals the length of the radius. Welcome to this free lesson guide that accompanies this Arc Length and Sector Area Explained! or A = rl / 2 square units. As indicated above, if you don't know the central angle, you have to know the radius and the arc length. Watch and learn how to find the area of a given sector of a circle. About this resource . Given, Question 8 : Find the area of the sector whose radius is 20 cm and perimeter is 110 cm. Solution : The given values. For example, if the arc length is 5 cm and the radius is 8 cm, your new numerator will be 40. How do I find the area of a segment that does not have degrees? Measuring the diameter is easier in many practical situations, so another convenient way to write the formula is (angle / 360) x π x (diameter / 2)2. 350 divided by 360 is 35/36. The area of the circle is equal to the radius square times . The following video lesson covers topics including: using the arc length and sector area equations to solve real-world problems. That gives you the sector area. By signing up you are agreeing to receive emails according to our privacy policy. If the angle is 360 degrees then the sector is a full circle. © MashUp Math, LLC | All Rights Reserved | Privacy Policy | Copyright Information |Contact, Arc Length and Sector Area Explained! All tip submissions are carefully reviewed before being published, This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. The area of a sector along an arc is also known as the circular sector. Explanation: . To calculate the area of a sector, start by finding the central angle of the sector and dividing it by 360. Then, the area of a sector of circle formula is calculated using the unitary method. A sector is an area formed between the two segments also called as radii, which meets at the center of the circle. Watch and learn how to find the area of a given sector of a circle. Keywords: sector; area; radius; solve for sector; pi; shaded region; central angle; Background Tutorials. Apart from that it is helpful in mathematical geometry problems etc. Multiplying Polynomials: The Complete Guide. By using this service, some information may be shared with YouTube. To find the area of a sector of a circle of radius of 4 centimeters and central angle measure of : Step 1: Find the area of the circle. Find the Radius of a Circle . Questions 1: For a given circle of radius 4 units, the angle of its sector is 45°. where 'l' is the length of the minor arc AB. What is the central angle if the radius is 7 cm and the area of a sector is 15 cm squared? The Best Free Printable 5th Grade Math Worksheets (and Answers! Calculate the area of a slice of pizza when the chef made all the slices with an angle of 45° b. by Anthony Persico. Please also find in the section below several worksheets and solutions on this topic to help your understanding. Please consider making a contribution to wikiHow today. You can often find me happily developing animated math lessons to share on my YouTube channel . Please input radius of the circle and the central angle in degrees, then click Calculate Area of Sector button. Examples to find the angle of a sector given its area or arc length. What is the area of a sector bounded by an arc of 60 degrees with a radius of 3 feet? Tutorial where you will learn the answers to the following key questions and information: What is the arc length formula? For example, if the central angle is 100 degrees, you will divide 100 by 360, to get 0.28. In this video, I explain the definition of a sector and how to find the sector area of a circle. A sector is a part of a circle that is shaped like a piece of pizza or pie. So the area of the sector over the total area is equal to the degrees in the central angle over the total degrees in a circle. Calculate the area of a sector when the angle made by the radii is 60° A = 60° / 360° × 3.14 × 5 2. Using this formula, and approximating , the area of the circle is . Videos, worksheets, 5-a-day and much more This article has been viewed 122,271 times. In addition to the radius, you need to know either the degree of the central angle, or the length of the arc. Let this region be a sector forming an angle of 360° at the centre O. The angle between the two radii is called as the angle of surface and is used to find the radius of the sector. Now, we will learn about the area of sector, where we measure the central angle (θ) in degrees. Read more. Sector. Every day at wikiHow, we work hard to give you access to instructions and information that will help you live a better life, whether it's keeping you safer, healthier, or improving your well-being. How to Calculate The Area of Sector with This Tool? But, if we measure the angle of a circle in radians, the area of sector formula will be AreaofSectorAreaof… What Is The Area of Sector Formula? To find the segment area, you need the area of triangle IDK so you can subtract it from the area of sector IDK. You'll see how to use given information and the formula for the area of a sector to find the answer. About Arc Length & Sector Area. In the case of arc length and sector area, you will only be dealing with a portion of a circle. How to use Area of a Sector Calculator? The total area of a circle is πR 2 corresponding to an angle of 2π radians for the full circle. formula to find sector area = (π r 2 θ) / 360. substitute the values. How can I find the area of a sector of a circle? If you're seeing this message, it means we're having trouble loading external resources on our website. Whenever you want to find area of a sector of a circle (a portion of the area), you will use the sector area formula: Where θ equals the measure of the central angle that intercepts the arc and r equals the length of the radius. You cannot find the area of a sector if you do not know the radius of the circle. Note: Trying to find the area of a sector of a circle? Just kidding! We can use this to solve for the circumference of the circle, , or . Our area of a sector calculator can be used to find sector area of a pizza, dress, land or whatever you want. What is the sector area formula? See how to find the area of the sector (blue area). To find the segment area, you need the area of triangle IDK so you can subtract it from the area of sector IDK. The formula to find the area of a sector is A = N/360 x (pi x r^2). The only two ways of finding a sector's area are shown above. Then, the area of a sector of circle formula is calculated using the unitary method. What is the arc length equation? Standard questions with diagrams progressing to worded questions. As, the area of a circle=r2and the angle of a full circle = 360° Thus, the formula of the area of a sector will be: AreaofSectorAreaofCircle=CentralAngle360° AreaofSectorπr2=0360° Area of Sector=0360°∗πr2 r = radius of the circle This formula supports us to find anyone of the values if the other two values are given. Before you can use the Sector Area Formula, you will have to find the value of θ (the central angle that intercepts arc AB, which is the arc of the shaded region ) and the length of the radius of circle K. Now, we know both our variables, so we simply need to plug them in and simplify. Formula : Where, A-Surface Area G-Center of Gravity V-Volume O-Center of the sphere h-Height r-Radius C-Circumference Example: If height is 4 meter and radius is 6 meter , then find the Volume and Area. If the angle is θ, then this is θ/2π the fraction of the full angle for a circle. The following is the calculation formula for the area of a sector: Where: A = area of a sector π = 3.141592654 r = radius of the circle θ = central angle in degrees. To find the area of the sector of a circle of radius 2 centimeters and central angle measure of radians. If the angle is 180 degrees then the sector is a semi-circle. Formula to find perimeter of the sector is = l + 2r. This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. To understand how to calculate the area of such a sector, it’s important to understand the formula that it uses, which is given above. 5 Awesome (and 100% Free) 6th Grade Algebra Resources! So we have to use the second formula to find the area of the given sector. How to Calculate the Area of a Sector of a Circle. Formula to find length of the arc is l = θ/36 0 ° ⋅ 2 ∏ r. Formula to find area of sector is A = θ/360 ° ⋅ ∏r 2 square units. In the formula given, A is the area of the sector, N is the degree of the central angle of the sector, pi is an irrational number that can be rounded to 3.14, and r is the length of the radius of the circle. Then, multiply the two numbers to get the area of the sector. Evaluating Expressions . The angle of the sector is 150º. or A = rl / 2 square units. Example 1: A sector is cut from a circle of radius 21 cm. Circle sector area calculator - step by step calculation, formulas & solved example problem to find the area of circle sector given input values of corcle radius & the sector angle in degrees in different measurement units between inches (in), feet (ft), meters (m), centimeters (cm) & millimeters (mm). Python Math: Exercise-8 with Solution. This Complete Guide to Arc Length and Sector Area includes several examples, a step-by-step tutorial, an animated video mini-lesson, and a free equation of a circle worksheet and answer key. Please consider making a contribution to wikiHow today. The area of a circle is the number of square units it takes to fill up the inside of the circle. You don't. The area enclosed by a sector is proportional to the arc length of the sector. Find the area of sector IDK. Solution : radius = 20 cm Anthony is the content crafter and head educator for YouTube's MashUp Math. For more on this seeVolume of a horizontal cylindrical segment. Sol. In the formula given, A is the area of the sector, N is the degree of the central angle of the sector, pi is an irrational number that can be rounded to 3.14, and r is the length of the radius of the circle. In this case the angle is [(15 cm²)(360°)] / [(3.14)(7² cm²)] = 35.1°. But what about θ ? A sector of a circle is essentially a proportion of the circle that is enclosed by two radii and … Since you are finding the area, the answer will be in square centimeters. You'll see how to use given information and the formula for the area of a sector to find the answer. You may have to do a little preliminary mathematics to get to the radius. The radius is the length from the center of a … the whole circle = \(πr^2\) When the angle is 1°, area of sector … Please help us continue to provide you with our trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker. Sol. A sector is a section of a circle. To calculate the sector area, first calculate what fraction of a full turn the angle is. https://www.bbc.com/bitesize/guides/zwcqcj6/revision/2, https://www.youtube.com/watch?v=cAOVS2DTU0U, http://www.mathopenref.com/arcsectorarea.html, https://www.onlinemath4all.com/how-to-find-the-area-of-the-sector.html, Calcolare l'Area di un Settore di un Cerchio, consider supporting our work with a contribution to wikiHow. Tutorial, The Best Free Math Worksheets for 1st Grade Students. Plug the sector's central angle measurement into the formula. Step 2: Use the proportional relationship. The formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2; But where does it come from? Share your thoughts in the comments section below! Example 1 : Find the perimeter of the sector PQR shown below. Find the area of circle segment IK. Draw an altitude straight down from D to segment IK. Circle; Perimeter; Polygons; Quadrilaterals; Special Points; Discover Resources. Then check out this tutorial! The arc length l and area A of a sector of angle θ in a circle of radius r are given by How do I find the angle of a sector if I have arch length and radius? Example 1 : Find the perimeter of the sector PQR shown below. Relate the area of a sector to the area of a whole circle and the central angle measure. Divide the length of the arc by the length of the circumference. Now that you know the value of θ and r, you can substitute those values into the Arc Length Formula and solve as follows: Notice that this question is asking you to find the area of a sector of circle K, so you will have to use the Sector Area Formula to solve it! A circle has a radius of 5 cm. 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