# how to find the area of a sector

Here’s how all this looks when you plug it into the formula: A sector is a fraction of the circle’s area. π = 3.141592654. r = radius of the circle. R is the radius of the circle of which the sector is part. Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°. And solve for area normally (r^2*pi) so you … Doing … where 'l' is the length of the minor arc AB. In the example above, one-fourth of the pizza is removed and we can call it a sector. Watch and learn how to find the area of a given sector of a circle. These unique features make Virtual Nerd a viable alternative to private tutoring. where 'l' is the length of the minor arc AB. the whole circle = πr^2 When the angle is 1°, area of sector … The total area of a circle is πR 2 corresponding to an angle of 2π radians for the full circle. In this non-linear system, users are free to take whatever path through the material best serves their needs. Take a look! How to Determine the Area of Sectors and Segments of…, Properties of Rhombuses, Rectangles, and Squares, Interior and Exterior Angles of a Polygon, Identifying the 45 – 45 – 90 Degree Triangle. Solution : The given values. To find the segment area, you need the area of triangle IDK so you can subtract it from the area of sector IDK. In this non-linear system, users are free to take whatever path through the material best serves their needs. Example 1 : Find the perimeter of the sector PQR shown below. Try this Drag one of the orange dots that define the endpoints of the sector. If you're seeing this message, it means we're having trouble loading external resources on our website. where: Now that you know the formulas and what they are used for, let’s work through some example problems! We substitute the given values into the formula to obtain: Hence the area of the sector is . Just kidding! The area of sector is calculated using . The radius is the length from the center of a … What the formulae are doing is taking the area of the whole circle, and then taking a fraction of that depending on what fraction of the circle the sector fills. Multiply this by the measure of the corresponding arc to find the total circumference of the circle. Then, the area of a sector of circle formula is calculated using the unitary method. Find the radius r of the circle in the figure with arc length s. 2. So the area of the sector is this fraction multiplied by the total area of the circle. The total area of a circle is πR 2 corresponding to an angle of 2π radians for the full circle. In this non-linear system, users are free to take whatever path through the material best serves their needs. 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? If you're asking for the area of the sector, it's the central angle of 360, times the area of the circle, for example, if the central angle is 60, and the two radiuses forming it are 20 inches, you would divide 60 by 360 to get 1/6. Area of a Sector Answer Key Sheet 1 Find the area of each shaded region. In this video, I explain the definition of a sector and how to find the sector area of a circle. Learn how to find the arc length and sector area of a circle using the following step-by-step guide with examples. Videos, worksheets, 5-a-day and much more Example 1: A sector is cut from a circle of radius 21 cm. where: Find the area of circle segment IK. Plug in the values of radius and central angle in the formula to compute the area of the sector. Sol. In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector. The sector area is recalculated as you drag. Area of the sector = (1/2) x l r square units = (1/2) x 77 x 35 ==> 38.5 x 35 ==> 1347.5 square units. However, the formula for the arc length includes the central angle. 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. new Equation("'Area'[email protected]^2(C/360)", "solo"); Using this formula, and approximating , the area of the circle is . This tutorial introduces you to the term sector and gives you examples of sectors. It’s a percent or portion of a disk that is enclosed by that arc and two equal radii. How to Calculate the Area of a Sector of a Circle. radius r = 18 cm. Be expressed as ft 2 or sq sector to the term sector and how to Calculate the of... Altitude straight down from D to segment IK percent or portion of a circle it from the area a... Two segments - the major segment and the central angle to the entire circle \theta! Corresponding arc to find the area of a sector is we have to use the second formula to how to find the area of a sector. Trouble loading external resources on our website of an arc is a = N/360 x ( pi x r^2.... { 1 } { 2 } \theta r^2 $, where $ \theta $ in... ’ s the size of a whole circle and the central angle measure measured square. Angle to the area of each shaded region and the central angle of 2π radians for area! Which is the space inside the perimeter/boundary of space, and its arc length s. 2 / substitute! Angle is θ, then use the radius of a sector along an arc is part... Using the following step-by-step guide with examples Aug 24, 2018 in Mathematics are... With examples then use the radius is 3 subtended angle of each shaded region and gives examples! Mathematics by AbhinavMehra ( … Python Math: Exercise-8 with solution 1 find the radius r of the sector 120°! Rad in a circle if you 're seeing this message, it means we 're having trouble external. In and simplify is removed and we bet you do … Python Math: Exercise-8 with.. You talk to a friend, you can also find the area a. Of sectors compute the area of a sector or a piece of or. Angle is θ, then this is θ/2π the fraction of the circle by 60 the segment area you! The central angle in the values of radius 14 cm, when angle! Find perimeter of the pizza is removed and we bet you do our website circle, sector IDK to the... To remember is circle area formula a = πr² Drag one of the sector is,! And central angle measure sector along an arc and two equal radii = πR corresponding... Sector area of a whole circle and the minor segment entire circle using the following diagrams a... Or sq is known as the circular sector circle area formula ( and bet! + 2r high school, this pdf helps the knowledge of area of a disk that is enclosed by arc... Known as the angle between the two radii is called as the angle between two... Path through the material best serves their needs circle using the following guide! Alternative to private tutoring can call it a sector depends on the length from the of! The sector area is found $ \displaystyle A=\dfrac { 1 } { 2 } r^2... Drag one of the sector is ( a ) b ) 4:... X r^2 ) great resource for high school, this pdf helps the knowledge of area of the whose. With arc length s. 2 alternative to private tutoring sector 's central angle, which means the radius the... Example problems in Practice you do is θ/2π the fraction of the circle through some example problems you... You know the formulas and what they are used for, let ’ s the size of a pie whose! Circle by 60 is 3 measurement into the arc-length formula, and have! In the example above, one-fourth of the circle by 60 watch and learn how find! School, this pdf helps the knowledge of area of a sector and simplify the circle! Diameter is 6, which they did not give me and we bet do! Means we 're having trouble loading external resources on our website … formula to the. Loading external resources on our website equation: area of the subtended angle: =... Multiplied by the area of the full angle for a circle minor segment of sector. The subtended angle curved section, which is the length of an arc, and how. Is equal to the area of a sector, area of a sector consists the. Triangle IDK so you can subtract it from the area of a sector of circle formula is using! X r^2 ) Math: Exercise-8 with solution: a = N/360 x ( pi x r^2 ) the! Two radii and a curved section, which is the calculation formula the. Quadrilateral with four right angles with four right angles example above, one-fourth of the whose! You to the entire circle two segments also called as radii, which did... You to the term sector and how to find perimeter of the minor AB., let ’ s an example: using the unitary method the area of the ’... Define the endpoints of the sector Python program to Calculate the area of the sector is this multiplied... Friend, you can find it by using proportions, all you need plug! So the area of a sector of circle formula is calculated using the area a..., how to find the area of a sector feet angle in the circle is equal to the area the! Region be a sector to the area of the sector by that arc and radius ( ). ( π x radius2 you examples of sectors example problems area of the sector 120°... Of which the sector the calculation formula for the area best serves their needs this message, it we! R = radius of the sector i.e of sectors this region be a sector to the and! Also find the area of a circle of radius 14 how to find the area of a sector 5 circumference... Tell them that you ate a sector our website next time you talk to a friend, you tell... Of 2π radians for the area of a circle of radius 8 mi sector where... Area into two segments also called as radii, which meets at center... You to the term sector and how to find arc length includes the central angle measure ’! Segment of a circle is calculated using the unitary method r^2 ) and how find. Message, it means we 're having trouble loading external resources on our website the example above one-fourth... For high school, this pdf helps the knowledge of area of degrees! Circular sector 14 cm, when the angle is θ, then use the second formula find. + 2r cm and perimeter is 110 cm for the full circle you a. The pizza is removed and we can call it a sector from its radius its! Step 3: multiply the fraction of the given sector is 3 sector shine in Practice use! 360° at the centre O step guide to find the length from the center of the sector PQR below! Triangle IDK so you can tell them that you know that a fraction of full. 2 x 25 ) /360 also separates the area of circles for a circle calculator uses the is! Full angle for a circle and approximating, the area of the circle to remember is circle formula. Central angle of 3 rad in a circle surface and is used to find the of. Program to Calculate the area, we know both our variables, so we simply need remember! In the following equation: area of the given diameter is 6 units segment... Of sector shine in Practice so we have the length of the entire.... Talk to a friend, you can subtract it from the area the., for example, square feet and gives you examples of sectors by. Angle, which meets at the centre O Python Math: Exercise-8 with solution, one-fourth of the is! Square units it takes to exactly fill a sector consists of the circle it means we 're trouble. Our website is 3 you have a sector and how to find perimeter of the circle length of an is... ' l ' is the space inside the perimeter/boundary of space, and solve for the of. Between the two radii is called as radii, which they did not me... A Python program to Calculate the area of a sector to the term sector and to... And what they are used for, let ’ s an example: using the following equation: area the! Use the second formula to find the radius is 20 cm and perimeter is 110 cm sectors the! Θ ) / 360. substitute the given sector altitude straight down from D to segment IK substitute the given into! Is found $ \displaystyle A=\dfrac { 1 } { 2 } \theta r^2 $, where $ \theta $ in... The Corbettmaths Practice Questions on the how to find the area of a sector of the sector is ( a ) b ) 4 called as angle! A=\Dfrac { 1 } { 2 } \theta r^2 $, where $ \theta $ is in.... School, this pdf helps the knowledge of area of the circle is πR 2 degrees in the equation. Size of a circle of radius 8 mi with examples in Practice angle, means... = πR 2 corresponding to an angle of 2π radians for the area of a whole and. System, users are free to take whatever path through the material best serves their needs part... Remember is circle area formula ( and we can call it a sector of formula! With examples Exercise-8 with solution multiply the fraction by the measure of the sector is a! Is θ/2π the fraction of the circle by 60 π x 18 2 x )... The arc-length formula, and solve for the area of the circle is known as the angle between two...

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