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.
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 calculate the area of a circle

To solve this problem, you must first introduce the concept of the number P (PI). The number P is a mathematical constant that expresses the ratio of the circumference to the diameter of this circle. P is an infinite non-periodic decimal fraction, its value is constant for all circles and is approximately 3,14159265358979... To solve practical problems is usually enough values of 3.14Area of the circle is one of the geometrical quantities determining its size. For finding this value is sufficient to know the radius of the circle and the number P (PI).
Instruction
1
Let there be a circle. If the radius of this circle we do not know, you can find it in several ways:
- to know the radius of a simple measurement of the radius of its circumference,
- if you know the circumference of this circle, its radius can be calculated according to the formula R = L/2P, where L is the length of the circumference,
- can you describe a square about a circle, then its radius is equal to half the side of the square.
2
From the school course of geometry known theorem - area of a circle is equal to half of the length of work limiting its circumference to the radius.
S = P*R*R
Note
There are several alternative formulas to calculate the area of a circle, all of them by way of transformation are reduced to a common formula, but may be useful in specific situations.

The area of a circle inscribed in a triangle.
S = P*((p-a)*tg(A/2))2, where p is pauperised, a, and A - side and the opposite angle of the triangle, respectively, (p-a)*tg(A/2) - radius of inscribed circle

The area of a circle described about the triangle.
S = P * (a/(2*sin(A)))2, where a and A - side and the opposite angle of the triangle respectively, a/(2*sin(A)) is the radius of the circumscribed circle.

Advice 3 : How to find the area, if you know the diameter

Knowing only the length of the diameter of the circle, you can calculate not only square the circle but also the square of some other geometrical figures. This follows from the fact that the diameters of the inscribed or circumscribed around the shapes of the circles coincide with the lengths of their sides or diagonals.
Instruction
1
If you need to find the area of a circle (S) for the length of its diameter (D), multiply the number PI (π) on the squared length of the diameter, and the result divide by four: S=2 π*D2/4. For example, if the diameter of the circle is twenty inches, then its area can be calculated as: 3,142 * 202 / 4 = 9,86 * 400 / 4 = 986 square centimeters.
2
If you need to find the area of a square (S) on the diameter described around the circumference (D), construct the length of diameter square, and the result is split in half: S=D2/2. For example, if the diameter of the circumscribed circle is twenty inches, then the area of square can be calculated as: 202 / 2 = 400 / 2 = 200 square centimeters.
3
If the area of a square (S) you need to find the diameter of the inscribed circle (D), it is enough to build the length of the diameter in square: S=D2. For example, if the diameter of the inscribed circle is twenty inches, then the area of square can be calculated as: 202 = 400 square centimeters.
4
If you need to find the area of a right triangle (S) according to the known diameterof the inscribed m (d) and described (D) circles around it, then build the length of the diameter of the inscribed circle in the square and divide by four, and to the result add half the product of the lengths of the diameters of the inscribed and circumscribed circles: S=d2/4 + D*D/2. For example, if the diameter of the circumscribed circle is twenty inches, and inscribed to ten centimeters, then the area of the triangle can be calculated as: 102 / 4 + 20*10/2 = 25 + 100 = 125 square centimeters.
5
Use the built in Google calculator to perform the necessary calculations. For example, to calculate a search area of a right triangle according to the example of the fourth step, it is necessary to enter a search query: "10^2 / 4 + 20*10/2", and then press the Enter key.

Advice 4 : How to find the area of a triangle inscribed in a circle

The area of a triangle can be calculated in several ways depending on which value is known from the conditions of the problem. If the base and height of triangle area can be found by calculating the work of half the base into altitude. In the second method the area is calculated using a circumscribed circle about a triangle.
Instruction
1
In problems of plane geometry is necessary to find the area of a polygon inscribed in a circle, or described about him. A polygon is considered to be described about the circle, if he is outside, and its sides touch the circle. The polygon inside the circle is considered to be inscribed in it, if its vertices lie on the circumference of the circle. If in the problem given a triangle inscribed in a circle that all three vertices touch the circle. Depending on what is considered a triangle, and selects the method of solving the problem.
2
The simplest case occurs when the circumference of the inscribed regular triangle. Since such a triangle all sides are equal, the radius of the circle is equal to half its height. Therefore, knowing the sides of a triangle, find its area. To calculate this area, in this case, you can use any of ways, for example:
R=abc/4S, where S is the area of the triangle a, b, c be the sidelengths of triangle

S=0.25(R/abc)
3
Another situation occurs when the triangle is isosceles. If the base of the triangle coincides with the diameter line of the circle or diameter is the height of the triangle, the area can be calculated in the following way:
S=1/2h*AC, where AC is the base of the triangle
If you know the radius of the circumcircle of an isosceles triangle, its angles, and the base coinciding with the diameter of a circle, the Pythagorean theorem can be found unknown height. The area of a triangle, whose base coincides with the diameter of a circle is equal to:
S=R*h
In another case, when the height is equal to the diameter of a circle circumscribed around an isosceles triangle, its area is equal to:
S=R*AC
4
The number of tasks in the circle is inscribed right triangle. In this case, the center of the circle lies in the middle of the hypotenuse. Knowing the angles and finding the base of the triangle, you can calculate the area of any of the methods described above.
In other cases, especially when the triangle is acute-angled or obtuse-angled, applicable only the first of the above formulas.

Advice 5 : How to measure the area of a circle

A circle is a simple geometrical figure that has no corners. If you measure the distance from the center of the circle to any extreme point, it will always be equal to the radius. The task typically requires to calculate the diameter and find the area of a circle. These indicators are easy to calculate if the radius of the circle is known.
You will need
• calculator.
Instruction
1
To find the area of the circle first, its radius lift to a square that is in the second degree. And then multiply the result by the number π (PI). If the problem is the radius given the diameter of the figure, can be split into 2. Now obtained by dividing the radius of the shapes use for the convenience of calculating the area of a circle.
2
To find the value of the square of the radius of a circle use a calculator. To start enter the value of radius of circle, then find a special button with the symbol x2. This symbol on the button shows that number to be raised to the second power. If you have any difficulty, multiply the radius of the circle on itself. To find the area of a circle, can use and diameter. The radius is ½ the diameter, and hence it can be represented as a fraction where the numerator is the value of the diameter, and in the denominator - 2. When computing the square of this fraction on a calculator, take the value of the diameter of the circle in the second degree, and then divide the resulting number by 4.
3
The value of the square of the radius of the circle , multiply by a factor of π (PI). To find the area of a circle, you can use a more exact or rounded value. To do this, enter the corresponding number (3,1415926535897932384626433832795 or 3.14). Often it is possible to use a special button marked with the symbol π (PI), as in many models of calculators.
4
The area of a circle is measure in square units. If the radius was given in centimeters (cm), area is expressed in square centimeters (cm2). When calculating radius from a diameter of the circle unit of measure does not change. For example, if the diameter were given in inches, then the radius will be measured in inches, and the desired area will be obtained in inches square. The problem is not always immediately specified radius. Sometimes initially given diameter of the circle. If you ignore this and use the diameter for calculations instead of the radius, the inevitable errors in calculations. To find the radius, the size of the diameter divide by 2.
To calculate the area of a circle use the number π (PI) is approximately equal 3,1415926535897932384626433832795. If greater accuracy is not required, you can round this factor to 3.14.

Advice 6 : 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.
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 7 : How to find the area, knowing the diameter

Objectives to calculate the area of a circle often meet in the school geometry course. To find the area of a circle, you need to know the length of the diameter or radius of a circle in which it is enclosed.
You will need
• - the length of the diameter of the circle.
Instruction
1
A circle is a figure in the plane consisting of a plurality of points disposed in the same distance from another point called the centre. A circle is a flat geometric figure, represents the set of points enclosed in a circle which is the boundary of the circle. Diameter is a segment that connects two points on the circle and passing through its center. The radius is the segment connecting a point on the circle and its center. π — the number "PI", a mathematical constant that is the constant. It shows the ratio of the circumference to the length of its diameter. To compute the exact value of π is impossible. In geometry use the approximate value of this number: π ≈ 3,14
2
The area of a circle equals the product of the square of the radius to the number calculated by the formula: S=NR^2, where S is the area of the circle, R is the length of the radius of the circle.
3
From the definition of the radius, it follows that it is equal to half the diameter. Hence, the formula becomes: S=π(D/2)^2, where D is the length of the diameter of the circle. Substitute in the formula the value of the diameter, calculate the area of a circle.
4
The area of a circle is measured in square units — mm2, cm2, m2, etc. In what units is expressed you received the area of a circle depends on what units was the diameter of a circle.
5
If you need to calculate the area of a ring use this formula: S=π(R-R)^2, where R, r are radii of the outer and inner circumferences of the ring, respectively.