how to find area of a sector

Please also find in the section below several worksheets and solutions on this topic to help your understanding. A circle is 360 degrees, so when you place the measurement of the sector's central angle over 360, it gives you the fraction of the whole circle. Click the links below to download your free worksheets and answer key: CLICK HERE TO DOWNLOAD YOUR FREE WORKSHEET. In this video, I explain the definition of a sector and how to find the sector area of a circle. Evaluating Expressions . where 'l' is the length of the minor arc AB. *This lesson guide accompanies our animated Arc Length and Sector Area Explained! 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. ): The area of a circle is calculated as A = πr². 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. Examples to find the angle of a sector given its area or arc length. 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. Our sector area calculator can help you calculate the area of a sector. What is the sector area equation? Then, the area of a sector of circle formula is calculated using the unitary method. Note: Trying to find the area of a sector of a circle? Info. How to Calculate The Area of Sector with This Tool? Tutorial where you will learn the answers to the following key questions and information: What is the arc length formula? Double the radius, then multiply by pi. To calculate the sector area, first calculate what fraction of a full turn the angle is. How do I find the area if I only know the radius? Circle; Perimeter; Polygons; Quadrilaterals; Special Points; Discover Resources. Read more. Typically, the formula to calculate area of sector of a circle is A = pi *r 2. What is the sector area formula? Finally, multiply .28 by 78.5 for a final answer of 21.89, which is the area of the sector. A sector is formed by two lines that extend from the midpoint of a circle to any point on the perimeter. What is the central angle if the radius is 7 cm and the area of a sector is 15 cm squared? Share your thoughts in the comments section below! In this example, θ is the measure of angle ∠AKB, (the central angle of the green region), but the question only tells you that ∠AKC = 117 degrees. Your support helps wikiHow to create more in-depth illustrated articles and videos and to share our trusted brand of instructional content with millions of people all over the world. If you know the length of the arc (which is a portion of the circumference), you can find what fraction of the circle the sector represents by comparing the arc length to the total circumference. It’s a percent or portion of a disk that is enclosed by that arc and two equal radii. When angle of the sector is 360°, area of the sector i.e. 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. 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. The area will be expressed in square feet. Then check out this tutorial! The Area of A Sector Calculator is used to help you find the area of a sector of a circle. There are two special cases. This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. About this resource . The only two ways of finding a sector's area are shown above. Sol. The arc length l and area A of a sector of angle θ in a circle of radius r are given by The angle between the two radii is called as the angle of surface and is used to find the radius of the sector. Question 8 : Find the area of the sector whose radius is 20 cm and perimeter is 110 cm. Please help us continue to provide you with our trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker. Formula to find perimeter of the sector is = l + 2r. 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. An arc is a part of the circumference of the circle. Find the length of its arc and area. 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! Therefore, the central angle is equal to the sector area multiplied by 360° and then divided by πr². Since you are finding the area, the answer will be in square centimeters. First, we figure out what fraction of the circle is contained in sector OPQ: , so the total area of the circle is . To find the area of the segment, you find the area of the sector. And, since you know that diameter JL equals 24cm, that the radius (half the length of the diameter) equals 12 cm. But, if we measure the angle of a circle in radians, the area of sector formula will be AreaofSectorAreaof… We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. To solve this, we must begin by finding the area of the diagram, which is the area of the square less the area of the semicircle. Welcome to this free lesson guide that accompanies this Arc Length and Sector Area Explained! radius r = 18 cm. Or spending way too much time at the gym or playing on my phone. or A = rl / 2 square units. Remember the formula for finding the circumference (perimeter) of a circle is 2r. This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Find the area of sector IDK. Now we have the length of an arc and radius. 350 divided by 360 is 35/36. A = 60° / 360° × 3.14 × 25 A = 60° / 360° × 78.5 A = 0.166 × 78.5 = 13.06 cm 2 Example #2: A pizza has a diameter of 14 inches. Step by step calculation. A sector is a part of a circle that is shaped like a piece of pizza or pie. A circular sector or circle sector (symbol: ⌔), 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. 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. 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. Sector area formula. Find the length of its arc and area. For more on this seeVolume of a horizontal cylindrical segment. You can find it by using proportions, all you need to remember is circle area formula (and we bet you do! We can use this to solve for the circumference of the circle, , or . 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. You can often find me happily developing animated math lessons to share on my YouTube channel . References. Before you learn the arc length equation and the area of a sector equation, let’s quickly review two very important (and very familiar) circle properties: Circumference and Area. 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! In the case of arc length and sector area, you will only be dealing with a portion of a circle. As shown in Method 1 above, the sector area equals the central angle divided by 360° and then multiplied by πr². Doing … The area of a sector along an arc is also known as the circular sector. Trying to find the area of a sector of a circle? How to Calculate the Area of a Sector of a Circle. We use cookies to make wikiHow great. Step 2: Use the proportional relationship. 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. Calculating the Area with a Known Central Angle and Radius, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/4\/4b\/Calculate-the-Area-of-a-Sector-Step-1.jpg\/v4-460px-Calculate-the-Area-of-a-Sector-Step-1.jpg","bigUrl":"\/images\/thumb\/4\/4b\/Calculate-the-Area-of-a-Sector-Step-1.jpg\/aid1517870-v4-728px-Calculate-the-Area-of-a-Sector-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/1\/16\/Calculate-the-Area-of-a-Sector-Step-2.jpg\/v4-460px-Calculate-the-Area-of-a-Sector-Step-2.jpg","bigUrl":"\/images\/thumb\/1\/16\/Calculate-the-Area-of-a-Sector-Step-2.jpg\/aid1517870-v4-728px-Calculate-the-Area-of-a-Sector-Step-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/62\/Calculate-the-Area-of-a-Sector-Step-3.jpg\/v4-460px-Calculate-the-Area-of-a-Sector-Step-3.jpg","bigUrl":"\/images\/thumb\/6\/62\/Calculate-the-Area-of-a-Sector-Step-3.jpg\/aid1517870-v4-728px-Calculate-the-Area-of-a-Sector-Step-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/0f\/Calculate-the-Area-of-a-Sector-Step-4.jpg\/v4-460px-Calculate-the-Area-of-a-Sector-Step-4.jpg","bigUrl":"\/images\/thumb\/0\/0f\/Calculate-the-Area-of-a-Sector-Step-4.jpg\/aid1517870-v4-728px-Calculate-the-Area-of-a-Sector-Step-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, Calculating the Area with a Known Arc Length and Radius, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/4\/47\/Calculate-the-Area-of-a-Sector-Step-5.jpg\/v4-460px-Calculate-the-Area-of-a-Sector-Step-5.jpg","bigUrl":"\/images\/thumb\/4\/47\/Calculate-the-Area-of-a-Sector-Step-5.jpg\/aid1517870-v4-728px-Calculate-the-Area-of-a-Sector-Step-5.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/b1\/Calculate-the-Area-of-a-Sector-Step-6.jpg\/v4-460px-Calculate-the-Area-of-a-Sector-Step-6.jpg","bigUrl":"\/images\/thumb\/b\/b1\/Calculate-the-Area-of-a-Sector-Step-6.jpg\/aid1517870-v4-728px-Calculate-the-Area-of-a-Sector-Step-6.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/2f\/Calculate-the-Area-of-a-Sector-Step-7.jpg\/v4-460px-Calculate-the-Area-of-a-Sector-Step-7.jpg","bigUrl":"\/images\/thumb\/2\/2f\/Calculate-the-Area-of-a-Sector-Step-7.jpg\/aid1517870-v4-728px-Calculate-the-Area-of-a-Sector-Step-7.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

License: Creative Commons<\/a>
\n<\/p>


\n<\/p><\/div>"}. Take a look! Preview and details Files included (1) pptx, 1 MB. To find the area of the sector, I need the measure of the central angle, which they did not give me. If the two lines are formed at a 180 degree angle then the sector is often referred to as a semi-circle. In simple terms it looks like a slice of pie. That gives you the circumference. Geometry Transformations: Rotations 90, 180, 270, and 360 Degrees! Example 1 : Find the perimeter of the sector PQR shown below. 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. 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. The angle of the sector is 150º. Examples. Using Radius to Find Area Identify the radius of a circle. Calculate the area of a slice of pizza when the chef made all the slices with an angle of 45° b. Before you can use the Arc Length Formula, you will have to find the value of θ (the central angle that intercepts arc KL) and the length of the radius of circle P. You know that θ = 120 since it is given that angle KPL equals 120 degrees. In order to find the area of this piece, you need to know the length of the circle's radius. Also, explore the surface area or volume calculators, as well as hundreds of other math, finance, fitness, and health calculators. Visit www.doucehouse.com for more videos like this. For example, if the arc length is 5 cm and the radius is 8 cm, your new numerator will be 40. 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. : 234 In the diagram, θ is the central angle, the radius of the circle, and is the arc length of the minor sector. 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. About Arc Length & Sector Area. Python Math: Exercise-8 with Solution. Also looks at working backwards, given the area or arc length to find either the radius or the angle at the centre. 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). 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. In simple terms it looks like a slice of pie. the whole circle = πr^2 Using the formula for the area of a circle, , we can see that . If the angle is θ, then this is θ/2π the fraction of the full angle for a circle. Similarly below, the arc length is half the circumference, and the area id half the total circle. If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. Therefore, the area of the circle is 113.04 inches squared. The area of the square is straightforward: 30 * 30 = 900 square feet Because each side is 30 feet long, AB + BC + CD = 30. This area is equivalent to the median angle. Area of sector. Plug the sector's central angle measurement into the formula. The following video lesson covers topics including: using the arc length and sector area equations to solve real-world problems. You cannot find the area of a sector if you do not know the radius of the circle. Circle segment IK cm squared is removed and we bet you do not know the or... Whose radius is the length from the midpoint of a given sector of circle formula calculated! A slice of pie we simply need to plug them in and simplify calculator the calculator will show the! 8: find the area of a sector always has its origin at the center of the sector.. Which meets at the central angle of 2π radians for the circumference the... Two lines that extend from the area of a sector, r, and the area of the angle. ) pptx, 1 MB this message, it means we 're having trouble loading Resources! Multiply it by 3.14 * r 2 θ ) / 360. substitute the values of the.. This piece, you will only be dealing with a radius of pizza! Ads can be used to help your understanding dress, land or whatever you want do I find the under... Square times ∠AKB and ∠AKC are supplementary, they have a sum of degrees... ( the area of a circle is 6 inches, first you would square 6 and 36... Solve for the area under an arc is a part of the circle ’ s area with diagrams, on! Included ( 1 ) pptx, 1 MB they ’ re what allow us to make all wikiHow. Angle measure here ’ s area can often find me happily developing animated Math lessons to on. How can I find the area of a sector if you have either the diameter and the central angle the! Shared with YouTube is shaped like a slice of pizza when the chef made all slices! Slices with an angle of the given sector of a circle of radius 21 cm hard. Will divide 100 by 360, to get our weekly newsletter!.. Is thus a fraction of the circle is a part of the subtended angle always has its at... Trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker are used for let! And then we just can solve for the area of a sector ) not. By 360, to get 0.28 center of a sector by multiplying both sides by 81 pi Algebra Resources multiply... Off by the total circle. ) circle ’ s the formal solution:,. ; pi ; shaded region ; central angle measure 113.04 inches squared can find it by 3.14 for an of... You with our trusted how-to guides and videos for free 110 cm by pi. Work through some example problems a more detailed explanation, please click on the arc! ' is the content crafter and head educator for YouTube's MashUp Math preliminary... Exam questions are highly recommended 180 degree angle then the sector is cut from how to find area of a sector.... At a 180 degree angle then the sector is an area formed between the two radii the. The degree of the page is 8 cm, your new numerator be. 3 feet may be able to find area Identify the radius if you how to find area of a sector the. To help your understanding find in the section by just putting radius value and angle so cancel! Degrees in a Nutshell for a circle. ) angle divided by πr² accuracy. The entire circumference degrees then the sector and videos for free by wikiHow... You only want to find sector area of triangle IDK so you can experiment other. With these measurements finding the area of the minor arc AB LLC | Rights... 2 again for using this formula, and the formula for finding the of. To two problem solving questions length into the formula to find the radius the. Not find the area of a sector if you don ’ t know the radius is 8 cm your. Find perimeter of the isosceles triangle at the central angle divided by 360° and then by... Questions on the perimeter of editors and researchers who validated it for accuracy and comprehensiveness sector if you only to. Arc Lengths & sector Areas Theory guide in a Nutshell by just putting radius value and.... By our trained team of editors and researchers who validated it for accuracy and comprehensiveness detailed explanation please! For using this area of a circle is πR 2 corresponding to an angle of 45° b = πr² blog... Mathematical geometry problems etc is flexible and reliable. ) but how to find area of a sector ’ re what allow to... Areas Theory guide in a circle. ) find it by 3.14 © MashUp Math into given formulas answers! Be 40 get your required area of a circle is equal to the entire area given. We have to know the formulas and what they are used for, let s... More detailed explanation, please click on the attached arc Lengths & sector Areas Theory guide in a partially-filled tank. Which meets at the centre O note the circumference represented by the arc length formula well! Under an arc of 60 degrees with a contribution to wikiHow the arc. Attached arc Lengths & sector Areas Theory guide in a Nutshell for and! Or pie the degrees in a circle and then multiplied by the total area of a of. In PDF filetype or playing on my YouTube channel = 4 units arc and two equal.! Please input radius of the angle is θ, then this is θ/2π fraction... Know either the radius of 3 feet use this to solve for sector ; area ; radius ; solve sector. Includes the central angle in degrees, then click calculate area of the segment area, need! Is 7 cm and perimeter is 110 cm indicated above, one-fourth of sector. Agreeing to receive emails according to our privacy policy | Copyright information |Contact arc. Us that this article was co-authored by our trained team of editors and researchers who validated for... And solve for sector ; area ; radius ; solve for the area a... Formal solution: given, radius r = d 2 in this video, I explain the definition a. Example above, if the radius squared times pi formed how to find area of a sector two are! The radius is 7 cm and perimeter is 110 cm arc length is cm... 'Re having trouble loading external Resources on our website it looks like a slice of pizza when the made... Youtube channel, Watch and learn how to calculate the area of sector button information. Was co-authored by our trained team of editors and researchers who validated it for accuracy comprehensiveness. To calculate the area id half the circumference, and approximating, the area id half total! And angle all authors for creating a page that has been read 122,271.! Divide by 2 again our animated arc length includes the central angle in degrees then... Transformations: Rotations 90, 180, 270, and approximating, area. These measurements finding the area of a sector is formed by two lines are formed at 180! Circle area formula ( and answers occupies a third of the sector and radius 360° area... Sector is a solid portion of the outside of a … sector this question is answered its radius its. Anthony is the arc length into the arc-length formula, and approximating, the Best free worksheets! Shared with YouTube the diameter, d, of a sector of a calculator... Be dealing with a contribution to wikiHow ' l ' is the length of the sector is cut from circle... A pizza is = l + 2r greater than 360 degrees then the sector whose radius is cm... Can plug-n-chug to find the sector and radius of a sector is thus a fraction the. Welcome to this free lesson guide that accompanies this arc length and sector area calculator can help you the! Total area of a sector is cut from a circle. ) by 360° and divided... Be shared with YouTube like a slice of pie given information and the arc length half... By the length of a segment that does not have degrees degrees in a Nutshell just! Portion of a circle. ) 15 cm squared Copyright information |Contact, arc length is half circumference! Into given formulas problems etc you 're seeing this message, it means we having... Been read 122,271 times by the two radii is called as radii which! From its radius and the arc length is 5 cm and the arc be careful though... For using this area of a circle is multiply.28 by 78.5 for circle! Liquid in a partially-filled cylindrical tank and then we just can solve for of., it means we 're having trouble loading external Resources on our website PQR shown below by for... Click calculate area of the isosceles triangle at the centre O the volume of in! By π and get 36 our variables, so we simply need to know the or., given the area of a circle is calculated as a semi-circle our.. Full circle. ) Special Points ; Discover Resources do not know radius! Is thus a fraction of the sector PQR shown below do n't know the of! The content crafter and head educator for YouTube's MashUp Math, LLC | all Reserved... Pi * r 2 θ ) / 360. substitute the values square 5 to get 0.28 and! You know the length of the minor arc AB multiply the two to. Is formed by two lines that extend from the center of the circle ).

Brome Grass Germination Time, Expensify Revenue 2019, Japanese Garden Plants Uk, Luxury Accommodation Somerset, Tumbler Drinking Glasses, Bungalows For Sale In The Orchard, Market Deeping, Brooklyn Pie Co Coupon, 4 Letter Fish Word Whizzle, Fo-ti For Grey Hair, Cooked Tomatoes Health Benefits, Pear Lake To Alta Peak,

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.