Advice 1: How to find the area of a semicircle

The need to find the area of a semicircle or sector occurs regularly in the design of architectural structures. This could be useful when calculating the tissue, for example, in the knight or musketeer cloak. In geometry there are different tasks to compute this parameter. The conditions may be asked to determine the area of a half circle, constructed on a particular side of the triangle or parallelepiped. In these cases, the required additional calculations.
How to find the area of a semicircle
You will need
  • - the radius of the semicircle;
  • - the range;
  • a pair of compasses;
  • - a sheet of paper;
  • pencil;
  • the formula for the area of a circle.
Instruction
1
Construct a circle with a given radius. The center of its label as a: to get a semi-circle, enough to hold through this point cut to the intersection with the circle. This cut is the diameter of this circle and equal to two radii. Remember what circumference and what is the circle. A circle is a line all points of which are removed from the center at the same distance. Circle the part of the plane bounded by this line.
2
Remember the formula for area of a circle. It is equal to the square of the radius multiplied by the constant factor π = 3.14. That is, the area of a circle expressed by the formula S=πR2, where S is the area and R is the radius of the circle. Calculate the area of a semicircle. It is equal to half the area of a circle, i.e. S1= πR2/2.
3
In case you are in conditions given the circumference, find the radius first. The circumference is calculated by the formula P=2nr. Accordingly, to find the radius should be the circumference divided by twice the coefficient. It turns out the formula R=P/2π.
4
The semicircle can be represented as a sector. A sector is a portion of a circle, which is limited by two radii and an arc. The size of the sector is equal to the area of the circle multiplied by the ratio of Central angle to a full angle of a circle. That is, in this case it is expressed by the formula S=π*R2*n°/360°. The sector angle is known, it is 180°. Substituting its value, you'll get the same formula is S1= πR2/2.
Note
There are tasks, where the arc angle is not in degrees but in radians. In this case, you must use the conversion formula Ar = Ad *π / 180°, where Ar is the angle in radians, and Ad — he is in degrees. To compute the area of a semicircle is not particularly important. Even if you are a semi-circle as a sector, in the final formula no degree no. But it may be necessary to compute the area of the sector that has a different Central angle.

In some problems it is required to find the area of a circle or semicircle, constructed on a particular side right or wrong polygon. Without additional constructions in this case can not do. It is necessary to divide a given shape into the other, whose parameters you specified, or you can easily find them. After that, calculate the desired direction, which often represents the diameter of a circle or semicircle.

Advice 2: How to find the area of a circle and its parts

Calculating area of a circle and its parts refers to the geometry problems 9th grade. The ability to solve them you may need not only to help your child with geometry, but also to perform technical tasks at work or at home. Applying the formula to calculate the area of a circle can, for example, to calculate the consumption of materials according to drawings in the construction of a circular pool or calculate the cross-sectional area of the electrical cable when performing electrical work.
How to find the area of a circle and its parts
You will need
  • To find the area of a circle:
  • - geometric formula for finding the area of a circle S = Пхг2, where:
  • - S - the area of a circle;
  • - P - the number "PI", it is constant and equal to the value of 3.14;
  • - r is the radius of the circle.
  • To find the area of sector of a circle:
  • geometric formula S=P x r2 / 360° x n°, where:
  • - S - the area of a sector of a circle;
  • - P - the number "PI", it is constant and equal to the value of 3.14;
  • - r - the radius of the circle;
  • - n - value Central angle of the sector in degrees.
Instruction
1
Measure the radius of the circle with a ruler. Calculate the value of the area of a circle by the geometric formula for finding the area of a circle (area of a circle equals the product of PI and the square of the radius of the circle).
2
Erect for finding the area of a circle the length of the radius of the circle in the square, multiply the resulting number by the number "PI" (its value is constant and equal to 3.14). So, using the formula you find the area of a circle.
3
Measure the sector angle in degrees with a protractor. The area of a circle you already know. Calculate the value of area of sector of a circle the formula for the geometric (area of sector of a circle equals the area of a circle with radius r on the ratio of sector angle n° to the angle in a full circle, i.e. 360°).
4
Divide the value of the area of a circle by 360 and multiply by the size of the sector angle in degrees. So you will find the amount of area of sector of circle degree measure of its angle.
Note
The radius is the segment connecting the center with any point on the circle(the circle). Diameter is a segment that connects two points on the circle (the circle) and passing through its center.

The circle sector is the portion of the circle bounded by an arc and two radii.

The Central angle of the sector is the angle formed by two radii.
Useful advice
To calculate the radius of a circle knowing its diameter, it is possible, by dividing the value of the diameter of the circle on the number 2.
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