{"id":8940,"date":"2021-12-09T22:31:40","date_gmt":"2021-12-09T17:01:40","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8940"},"modified":"2022-01-16T17:12:12","modified_gmt":"2022-01-16T11:42:12","slug":"segment-of-a-circle-area","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/segment-of-a-circle-area\/","title":{"rendered":"Segment of a Circle Area – Formula and Examples"},"content":{"rendered":"

Here you will learn what is the formula for major and minor segment of a circle to find its area with examples.<\/p>\n

Let’s begin –<\/p>\n

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

A segment of a circle is defined as the part of circle bounded by a chord and the arc.<\/p>\n

In the figure, the part APB is a segment of circle.<\/p>\n

Area of Segments Formula<\/h2>\n

Let AB be a chord of circle with radius r. Let \\(\\angle\\) AOB = \\(\\theta\\) and 0 < \\(\\theta\\) 180.\"segment<\/p>\n

The minor segment corresponding to chord AB is shown in figure.<\/p>\n

Area of Minor Segment = Area of sector OAB – Area of triangle OAB<\/p>\n

Since area of sector = \\(\\theta\\over 360\\) \\(\\pi r^2\\) and <\/p>\n

area of triangle = \\(1\\over 2\\) \\(r^2 sin\\theta\\)<\/p>\n

\n

Hence, Area of Minor Segment = \\(\\theta\\over 360\\) \\(\\pi r^2\\) – \\(1\\over 2\\) \\(r^2 sin\\theta\\)<\/p>\n<\/blockquote>\n

Area of Major Segment = Area of Circle – Area of Minor Segment<\/p>\n

\n

Hence, Area of Major Segment = \\(\\pi r^2\\) – ( \\(\\theta\\over 360\\) \\(\\pi r^2\\) – \\(1\\over 2\\) \\(r^2 sin\\theta\\))<\/p>\n<\/blockquote>\n

Example<\/strong><\/span> : A chord 10 cm long is drawn in a circle whose radius is \\(\\sqrt{50}\\) cm. Find the area of segments.<\/p>\n

Solution<\/span><\/strong> : Radius of the circle = \\(\\sqrt{50}\\) cm<\/p>\n

\\(\\therefore\\)   Area of circle = \\(22\\over 7\\) \\(\\times\\) \\((\\sqrt{50})^2\\) = \\(1100\\over 7\\) = 157.14 \\(cm^2\\)<\/p>\n

Since, OA = OB = \\(\\sqrt{50}\\) cm<\/p>\n

\\((OA)^2\\) + \\((OB)^2\\) = 50 + 50 = 100 cm<\/p>\n

\\((AB)^2\\) = 100<\/p>\n

\\(\\therefore\\)  \\((OA)^2\\) + \\((OB)^2\\) = \\((AB)^2\\)  \\(\\implies\\)  \\(\\angle\\) AOB = 90<\/p>\n

Area of sector OAB = \\(90\\over 360\\) \\(\\times\\) \\(22\\over 7\\) \\(\\times\\)  \\((\\sqrt{50})^2\\) = 39.29 \\(cm^2\\)<\/p>\n

Area of triangle OAB = \\(1\\over 2\\) \\(r^2 sin\\theta\\) = \\(1\\over 2\\) \\(\\times\\) (50 sin 90) = 25 \\(cm^2\\)<\/p>\n

\\(\\therefore\\)  Area of Minor Segment = Area of sector OAB – Area of triangle OAB<\/p>\n

= 39.29 – 25 = 14.29  \\(cm^2\\)<\/p>\n

Area of Major Segment = Area of Circle – Area of Minor Segment<\/p>\n

= 157.14 – 14.29 = 142.85 \\(cm^2\\)<\/p>\n\n\n

\n
Previous – Sector of a Circle Area and Perimeter<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the formula for major and minor segment of a circle to find its area with examples. Let’s begin – What is the Segment of a Circle ? A segment of a circle is defined as the part of circle bounded by a chord and the arc. In the figure, …<\/p>\n

Segment of a Circle Area – 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":[717,716],"yoast_head":"\nSegment of a Circle Area - Formula and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula for major and minor segment of a circle to find its area with examples.\" \/>\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\/segment-of-a-circle-area\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Segment of a Circle Area - 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