Need to find the area of a semicircle or the sector arises regularly at design of architectural constructions. It can be necessary also when calculating fabric, for example, on a knightly or mushketersky raincoat. In geometry various tasks for calculation of this parameter meet. In conditions it can be offered to determine the area of the half-circle constructed on a certain party of a triangle or parallelepiped. In these cases additional calculations are necessary.
It is required to you
- - semi-circle radius;
- - ruler;
- - compasses;
- - sheet of paper;
- - pencil;
- - formula of the area of a circle.
1. Construct a circle with the set radius. It designate the center as the Lake. To receive a semicircle, it is enough to carry out through this point a piece before crossing with a circle. This piece is diameter of this circle and is equal to two of its radiuses. Remember what is a circle and what is a circle. The circle is a line which all points are removed from the center on identical distance. A circle - the part of the plane limited to this line.
2. Remember a formula of the area of a circle. It is equal to the radius square increased by constant coefficient π, equal 3.14. That is the area of a circle is expressed by formula S=πR2 where S is the area, and R is circle radius. Calculate the area of a semicircle. It is equal to a half of the area of a circle, that is S1 = πR2/2.
3. In case you in conditions were given only circle length, find at first radius. Length of a circle is calculated on a formula P=2πR. Respectively, to find radius, it is necessary to divide length of a circle into the doubled coefficient. The formula R=P/2π turns out.
4. The semicircle can be presented and as the sector. The sector is called a part of a circle which is limited to its two radiuses and an arch. The area of the sector is equal to the area of a circle increased by the relation of the central corner to a full corner of a circle. That is, in this case it is expressed by formula S=π*R2*n °/360 °. The corner of the sector is known, it makes 180 °. Having substituted its value, you receive the same formula again - S1 = πR2/2.