The triangle is such a geometric shape, which consists of three straight lines connected at points that are not lying on one straight line. Points of connecting lines are the vertices of the triangle, which are denoted by Latin letters (for example, A, B, C). Connecting straight triangles are called segments that are also accepted by latin letters. The following types of triangles distinguish:
- Rectangular.
- Stupid.
- Acute.
- Versatile.
- Equilateral.
- Isosceles.
General formulas for calculating the triangle area
The formula of the triangle area in length and height
S \u003d A * H / 2,
Where and is the length of the side of the triangle, the area of \u200b\u200bwhich needs to be found, the H-length spent to the base of height.
Formula Gerona
S \u003d √R * (R - A) * (P-B) * (P-C),
where √ is a square root, the p-half-version of the triangle, A, B, C is the length of each side of the triangle. The half-period of the triangle can be calculated by the formula P \u003d (A + B + C) / 2.
The formula of the area of \u200b\u200bthe triangle in the magnitude of the angle and length of the segment
S \u003d (A * B * SIN (α)) / 2,
where b, c is the length of the parties of the triangle, Sin (α) is the sine of the angle between the two sides.
The formula of the area of \u200b\u200bthe triangle on the radius of the inscribed circle and the three sides
S \u003d P * R,
Where P is a half-versioner of a triangle, the area of \u200b\u200bwhich needs to be found, the R-radius inscribed in this triangle of the circle.
The formula of the triangle area for three sides and the radius of the circumference described around it
S \u003d (A * B * C) / 4 * R,
where A, B, C is the length of each side of the triangle, the R radius described around the triangle of the circle.
The formula of the area of \u200b\u200bthe triangle on the Cartesian coordinates of the points
Cartesian coordinates of points are coordinates in the Xoy system, where X is an abscissa, Y-ordinate. The decartian system of XOY coordinates on the plane is called mutually perpendicular numeric Ox axes and Oy with a total start of reference at O. If the coordinates of the points on this plane are specified in the form A (x1, y1), b (x2, y2) and c (x3, y3 ), then you can calculate the triangle area according to the following formula, which is obtained from the vector product of two vectors.
S \u003d | (x1 - x3) • (y2 - y3) - (x2 - x3) • (y1 - y3) | / 2,
where || Indicates the module.
How to find a square of a rectangular triangle
The rectangular triangle is such a triangle, which has one angle of 90 degrees. Such angle in a triangle can only be one.
The formula of the area of \u200b\u200bthe rectangular triangle in two categories
S \u003d a * b / 2,
Where a, B is the length of cathets. Cates are called the sides adjacent to the straight corner.
The formula of the area of \u200b\u200bthe rectangular triangle on hypotenuse and acute corner
S \u003d a * b * sin (α) / 2,
Where A, B are the katets of the triangle, and Sin (α) is a sine of an angle, in which straight a, b is intersect.
The formula of the area of \u200b\u200bthe rectangular triangle on the cathelet and the opposite corner
S \u003d a * b / 2 * tg (β),
where a, b is the katenets of the triangle, TG (β) is a tangent of an angle, in which the catts a, b are connected.
How to calculate an equal triangle area
It is an equally called such a triangle that has two equal sides. These parties are called side, and the other side is the basis. To calculate the area of \u200b\u200ban equilged triangle, one of the following formulas can be used.
The main formula for calculating the area of \u200b\u200ban equilibrium triangle
S \u003d H * C / 2,
where C is the base of the triangle, H is the height of the triangle, lowered to the base.
The formula of an equilibrium triangle on the side and base
S \u003d (C / 2) * √ (A * A - C * C / 4),
where C is the base of the triangle, the value of one of the lateral sides of an equifiable triangle.
How to find an equilateral triangle area
An equilateral triangle is such a triangle that all parties are equal. To calculate the area of \u200b\u200bthe equilateral triangle, you can use the following formula:
S \u003d (√3 * a * a) / 4,
where a is the length of the side of the equilateral triangle.
The above formulas will allow calculating the desired triangle area. It is important to remember that to calculate the spare triangles need to consider the type of triangle and the available data that can be used to calculate.
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