How to calculate the area of a triangle?

Sometimes in life there are situations where you have to dig into your memory in search of long-forgotten school knowledge. For example, you need to determine the area of a land plot in a triangular shape, or another repair in an apartment or a private house has come, and you need to calculate how much material will leave for a surface with a triangular shape. There was a time when you could solve such a problem in a couple of minutes, and now you are desperately trying to remember how to determine the area of the triangle?

Do not worry about it! After all, this is quite normal, when the human brain decides to shift long-unused knowledge somewhere to a remote corner, from which it is sometimes not so easy to extract them. So that you do not have to suffer with the search for forgotten school knowledge to solve such a problem, this article contains various methods that make it easy to find the desired area of the triangle.

It is generally known that a triangle is a kind of polygon that is bounded by the minimum possible number of sides. In principle, any polygon can be divided into several triangles by joining its vertices with segments that do not intersect its sides. Therefore, knowing the formulas for calculating the area of a triangle, you can calculate the area of almost any figure.

Among all possible triangles that occur in life, we can distinguish the following particular types: equilateral, isosceles and rectangular.

The simplest area of a triangle is calculated when one of its corners is straight, that is, in the case of a rectangular triangle. It's easy to see that it is half the rectangle. Therefore, its area is equal to half the product of the sides, which form a right angle.

If we know the height of a triangle, dropped from one of its vertices on the opposite side, and the length of this side, which is called the base, then the area is calculated as half the product of height on the base. It is written using this formula:

S = 1/2 * b * h, in which

S is the required area of the triangle;

B, h - respectively, the height and the base of the triangle.

So it is easy to calculate the area of an isosceles triangle, since the height will divide the opposite side in half, and it can easily be measured. If the area of a right-angled triangle is determined , then as the height it is convenient to take the length of one of the sides forming a right angle.

All this is certainly good, but how to determine if one of the angles of a triangle is straight or not? If the size of our figure is small, then you can use the building angle, drawing triangle, postcard or other object with a rectangular shape.

But what if we have a triangular plot of land? In this case, proceed as follows: the distance from the top of the assumed right angle on one side is a multiple of 3 (30 cm, 90 cm, 3 m), and on the other side, a distance multiple of 4 (40 cm, 160 cm, 4 m). Now you need to measure the distance between the end points of these two segments. If the result is a multiple of 5 (50 cm, 250 cm, 5 m), then we can say that the angle is straight.

If the length of each of the three sides of our figure is known, then the area of the triangle can be determined using the Heron formula. In order for it to have a simpler form, a new quantity is used, which is called a semiperimeter. This is the sum of all sides of our triangle, divided in half. After the half -perimeter is calculated, we can proceed to determine the area by the formula:

S = sqrt (p (pa) (pb) (pc)), where

Sqrt is the square root;

P is the semiperimeter value (p = (a + b + c) / 2);

A, b, c are the edges (sides) of the triangle.

But what if the triangle has an irregular shape? There are two possible ways. The first of them is to try to divide such a figure into two rectangular triangles, the sum of the areas of which are counted separately, and then folded. Or, if the angle between the two sides and the size of these sides are known, then apply the formula:

S = 0.5 * ab * sinC, where

A, b - sides of the triangle;

C is the magnitude of the angle between these sides.

The latter case is rare in practice, but nevertheless, everything is possible in life, therefore the above formula will not be superfluous. Good luck with your calculations!