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#### • how to find the area of half a circle

Question:Example: What is the area contained within a chord line that is 1" from the edge of a circle if the circle is 22" in diameter. I would like a nice easy formula for area when the chord is 1" from the edge, 2" from the edge, 3" from the edge.....etc.

Answers:You can work this out for yourself. The chord and 2 radii form a triangle. Because you know all 3 sides, you can calculate the angle at the centre between the 2 radii. Just drop a perpendicular from the centre of the circle to the midpoint of the chord to give you 2 right-angled triangles. The hypotenuse is the radius of the circle, half the chord is another side, and the ratio between the half-chord and the radius is the sine of the angle at the centre. Double this angle and you have the angle subtending the whole chord. The area of the sector (wedge) of the circle is proportional to the angle. You can find the area contained within the chord, the segment, by subtracting the area in the triangle from the area of the sector. As you see, you can make a formula of this, but it is not a simple one. Good luck.

Question:its not my homework but im trying to figure out whats written on my book. i dont get it. tnx.

Answers:The formula for the area of a circle is: A = pi * r^2 where r is the radius and is related to the diameter by r=d/2 So, if we plug in 22 for 'd', we get r = 11. We then stick this into the formula for the area and get: A = pi * 11^2 = pi * 121 Now we have the area of a circle with diameter 22. To find the area of the corresponding half circle, we just divide by 2: A = (pi*121)/2 If you are interested in where the formula A = pi*r^2 comes from, visit: http://www.worsleyschool.net/science/files/circle/area.html There is a short, good, and uncomplicated explanation.

Question:How do you find the perimeter and area of a half circle? you dont have to but say the diameter was 2.59 what would the p and a be?

Answers:Perimeter of a circleis = 2*pi*r (3.14 x 2.59 = 8.132) where pi is 22/7 or 3.14 and r stands for radius hich is half of diameter. For perimeter of half circle divide 2*pi*r by 2. That is 2 upon 2 gone and so formula for perimeter of half circle is pi*r (4.066) area of a circle = pi*r*r (3.14 x (1.295 x 1.295) =5.2658 ) so area of semi circle is (pi*r*r)/2= 2.6329

Question:I have a really tough question on my homework, any help is appreciated. What could I do to mathematically prove that the area of any sector of a circle with central angle '@' is A=1/2@r^2 (@ is the measure of the center angle in radians, r is radius, 1/2 is one half). It's a basic formula, but I can't think of any way other than example, and that won't work. Someone better at math, any suggestions?

Answers:If this a homework problem, for SURE the teacher expects you to figure it in this way: The area A of a full circle of radius r is: A = r A sector angle of is a fraction of the full circle of 2 . This fraction is / 2 The area S of the sector with central angle is that fraction of the full circle, or S = ( / 2 ) A = ( / 2 ) ( r ) = ( / 2) r Keep in mind that 360 degrees in radians is 2 . That's it. Addendum: Read the guy's answer below if you're taking a calculus class.

Area of Segment of a Circle :Check us out at www.tutorvista.com A circular sector or circle sector, is the portion of a circle enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. Its area can be calculated as described below. Let be the central angle, in radians, and r the radius. The total area of a circle is r2. The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and 2 (because the area of the sector is proportional to the angle, and 2 is the angle for the whole circle): Also, if refers to the central angle in degrees, a similar formula can be derived. A sector with the central angle of 180 is called a semicircle. Sectors with other central angles are sometimes given special names, these include quadrants (90 ), sextants (60 ) and octants (45 ). The length, L, of the arc of a sector is given by the following formula: where is in degrees. The length of the perimeter of a sector is sum of arc length and the two radii. It is given by the following formula: where is in degrees. The angle formed by connecting the endpoints of the sector to any point on the circle that is not in that sector is equal to half the arc length

Area of a Circle :Taking rozeboosje's idea and running with it a little. The technical term for the method employed in this video is called 'exhaustion' and is a basic form of calculus. Edit: The second to last slide has a formula that has omitted pi in error. This video does a better job explaining it and you get to use scissors - www.youtube.com