{"id":8931,"date":"2021-12-09T00:10:41","date_gmt":"2021-12-08T18:40:41","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8931"},"modified":"2022-01-16T17:12:05","modified_gmt":"2022-01-16T11:42:05","slug":"sector-of-a-circle-area-and-perimeter","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/sector-of-a-circle-area-and-perimeter\/","title":{"rendered":"Sector of a Circle Area and Perimeter – Formula and Examples"},"content":{"rendered":"

Here you will learn perimeter and area of sector of circle formula with examples.<\/p>\n

Let’s begin –<\/p>\n

What is Sector of a Circle ?<\/h2>\n

The region bounded by two radii of a circle and the arc intercepted by them is called a sector of the circle.\"sector<\/p>\n

A sector is measured by the angle which its arc subtends at the centre of the circle.<\/p>\n

Also Read<\/strong> : Formula for Length of Arc of Circle with Examples<\/a><\/p>\n

Perimeter of a Sector Formula<\/h2>\n
\n

Perimeter = 2r + \\(\\pi r \\theta\\over 180\\)<\/p>\n<\/blockquote>\n

Area of a Sector Formula<\/h2>\n
\n

Area = \\(\\theta\\over 360\\) \\(\\times\\) \\(\\pi r^2\\) = \\(\\pi r^2 \\theta\\over 360\\)<\/p>\n<\/blockquote>\n

When length of the arc (\\(l\\)) is given, then area of sector<\/p>\n

\n

Area = \\(1\\over 2\\) \\(lr\\)<\/p>\n<\/blockquote>\n

Example<\/strong><\/span> : A sector is cut from a circle of diameter 21 cm. If the angle of the sector is 150, find its area.<\/p>\n

Solution<\/span><\/strong> : We have,<\/p>\n

Diameter = 21 cm  \\(\\implies\\)  radius = \\(21\\over 2\\) cm<\/p>\n

Angle of sector = 150<\/p>\n

Area of the sector = \\(\\theta\\over 360\\) \\(\\times\\) \\(\\pi r^2\\) = \\(150\\over 360\\) \\(\\times\\) \\(22\\over 7\\) \\(\\times\\) \\(({21\\over 2})^2\\)<\/p>\n

= \\(5\\over 12\\) \\(\\times\\) \\(22\\over 7\\) \\(\\times\\) \\(21\\over 2\\) \\(\\times\\) \\(21\\over 2\\) = \\(5\\times 11\\times 21\\over 4\\times 2\\) = 144.38 \\(cm^2\\)<\/p>\n

Hence, the area of sector is 144.38 \\(cm^2\\)<\/p>\n

Example<\/strong><\/span> : The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.<\/p>\n

Solution<\/span><\/strong> : Let O be the centre with radius 5.6 cm, and let OAB be its sector(as shown in figure above) with perimeter 27.2 cm<\/p>\n

Then, OA + OB + arc AB = 27.2 cm<\/p>\n

\\(\\implies\\) 5.6 + 5.6 + arc AB = 27.2 cm<\/p>\n

\\(\\implies\\) arc AB = 16 cm<\/p>\n

Area of the sector OAB = \\(1\\over 2\\) \\(\\times\\) radius \\(\\times\\) arc length<\/p>\n

= \\(1\\over 2\\) \\(\\times\\) 5.6 \\(\\times\\) 16 = 44.8 \\(cm^2\\)<\/p>\n

Hence, the area of sector is 44.8 \\(cm^2\\)<\/p>\n\n\n

\n
Next – Segment of a Circle Area \u2013 Formula & Examples<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Formula for Length of Arc of Circle with Examples<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn perimeter and area of sector of circle formula with examples. Let’s begin – What is Sector of a Circle ? The region bounded by two radii of a circle and the arc intercepted by them is called a sector of the circle. A sector is measured by the angle which its …<\/p>\n

Sector of a Circle Area and Perimeter – Formula and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[63],"tags":[713,715,714],"yoast_head":"\nSector of a Circle Area and Perimeter - Formula and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn perimeter and area of sector of circle formula and examples based on it.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/sector-of-a-circle-area-and-perimeter\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sector of a Circle Area and Perimeter - 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