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Areas of Combined Figures Involving Circles

Calculate areas of irregular shapes.

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Credit: Kongsvinger Kommune
Source: http://www.flickr.com/photos/35097719@N07/3841882345
License: CC BY-NC 3.0

Where in the real world do you see combined figures? Why would you need to know how to find the area of combined figures involving circles? Well, if you've ever played basketball or wanted to join a basketball team, the dimensions of the court have everything to do with combined figures, circles, and area.

Why It Matters

There isn't anything random in the design of a basketball court. Courts are divided down the middle so that one side of the court is symmetrical to the other side. This balance ensures that the game is fair, with both teams having the same amount of room to play. The exact dimensions of the court depend on the skill level of the players. For example, the official courts used by players in the National Basketball Association (NBA) are probably larger than the courts at your school or local park. According to NBA guidelines, professional courts must measure 94 feet by 50 feet. High school courts have to be 84 feet by 50 feet, while middle school courts are 74 feet by 42 feet.

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

If you were assigned the task of designing a new court, you could change up the colors, choose where to add a logo, and decide on the style of basketball hoop—but you couldn't touch the math. The dimensions of the court must match the guidelines, from the location of the free-throw line to the area under the hoop. Notice that the area under the hoop is a combined figure. It is made up of a rectangle and half of a circle. As a designer, knowing how to work with these dimensions and combined areas ensures a fair game. As a player, knowing and making full use of the area of your playing space might spell the difference between victory and defeat!

See for yourself: http://www.youtube.com/watch?v=M6nNxtMGZsg

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Watch the videos below to review how to find the area of combined figures and to learn more about the dimensions of the NBA basketball court.



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Image Attributions

  1. [1]^ Credit: Kongsvinger Kommune; Source: http://www.flickr.com/photos/35097719@N07/3841882345; License: CC BY-NC 3.0
  2. [2]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0

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