In geometry classes in high school, we were all told how to find the area of a right triangle. However, as part of the school curriculum, we obtain only the most necessary knowledge and learn the most common and standard methods of computing. Are there any unusual ways to find this value?
As an introduction, let us recall which triangle is considered to be rectangular, and also denote the concept of area.
A rectangular triangle is a closed geometric figure, one of the corners of which is equal to 90 0 . The integral concepts in the definition of a right triangle are the legs and the hypotenuse. By legs, they mean two sides, which at a junction point form a right angle. Hypotenuse is the side opposite the right angle. A straight triangle can be isosceles (its two sides will have the same size), but it will never be equilateral (all sides are the same length). The definitions of height, median, vectors and other mathematical terms will not be discussed in detail. They are easy to find in directories.
The area of a straight triangle. Unlike rectangles, the rule of
product of the parties in determining the
area of the triangle is not valid. Speaking in the dry language of terms, then the area of a triangle is understood to mean the property of this figure to occupy a part of the plane, expressed by a number. Quite difficult to perceive, agree. We will not try to delve deeply into the definition, our goal is not that. We turn to the main thing - how to find the area of a right triangle? We will not perform the calculations ourselves; we indicate only formulas. To do this, we define the notation: A, B, C - sides of the triangle, legs - AB, BC. The angle of the ACB is straight. S is the area of the triangle, h
n n is the height of the triangle, where nn is the side on which it is lowered.
Method 1. How to find the area of a right-angled triangle, if the size of its legs is known
S = 0.5 * a * b
Method 2. Find the area of an isosceles right triangle
S = 0.5 * h BC * BC
Method 3. Calculation of the area through the rectangle
We build a right triangle to a square (if the triangle
isosceles) or rectangle. We get a simple quadrangle composed of 2 identical right-angled triangles. In this case, the area value of one of them will be equal to half the area of the resulting figure. S of the rectangle is calculated by the product of the sides. Denote this value M. The desired area value will be equal to half M.
S = 0.5 * M
Method 4. "Pythagorean pants." The famous Pythagorean theorem
We all remember its wording: "the sum of the squares of the legs ...". But not everyone can
to say, and what does this have to do with some “pants”. The fact is that initially Pythagoras studied the relationship of
squares of squares built on the sides of a straight triangle. Having revealed patterns in the aspect ratio of the squares, he was able to derive the formula known to all of us. It can be used when the value of one of the sides is unknown.
Method 5. How to find the area of a right-angled triangle using the Heron formula
Also a fairly simple method of calculation. The formula involves the expression of the area of a triangle in terms of the numerical values of its sides. For calculations, it is necessary to know the values of all sides of the triangle.
S = (p – AC) * (p – BC), where p = (AB + BC + AC) * 0.5
In addition to the above, there are many other ways to find the value of such a mysterious figure as a triangle. Among them: calculation by the method of an inscribed or described circle, calculation using the coordinates of the vertices, the use of vectors, absolute values, sines, tangents.