Sometimes in life there are situations when you have to delve into the memory in search of long-forgotten school knowledge. For example, you need to determine the area of a triangular-shaped land plot, or it’s the turn of the next repair in an apartment or private house, and you need to calculate how much material will go 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 a triangle?
Do not worry about it! After all, this is quite normal when the human brain decides to transfer long-unused knowledge somewhere to a remote corner, from which it is sometimes not so easy to extract. 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 well known that a triangle is a kind of polygon that is limited by the minimum possible number of sides. In principle, any polygon can be divided into several triangles, connecting 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 shape.
Among all the possible triangles that occur in life, the following particular types can be distinguished: equilateral, isosceles, and rectangular.
The easiest way to calculate the area of a triangle is when one of its angles is straight, that is, in the case of a right-angled triangle. It’s easy to see that it is half a rectangle. Therefore, its area is equal to half the product of the parties, which form a right angle between themselves.
If we know the height of the triangle, dropped from one of its vertices to the opposite side, and the length of this side, which is called the base, then the area is calculated as half the product of the height and the base. This is written using the following formula:
S = 1/2 * b * h, in which
S is the desired area of the triangle;
b, h - respectively, the height and base of the triangle.
It is so 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 a 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 corners of a triangle is straight or not? If the size of our figure is small, then you can use the construction corner, drawing triangle, postcard or other object with a rectangular shape.
But what if we have a triangular land? In this case, proceed as follows: count the distance multiple of 3 (30 cm, 90 cm, 3 m) from the top of the assumed right angle on one side, and measure the distance multiple of 4 (40 cm, 160 cm, on the other side) 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 it can be argued that the angle is straight.
If the length value 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 value is used, which is called a semi-perimeter. This is the sum of all sides of our triangle, divided in half. After the half-meter is calculated, you can proceed to determine the area according to the formula:
S = sqrt (p (pa) (pb) (pc)), where
sqrt is the square root;
p is the half-perimeter value (p = (a + b + c) / 2);
a, b, c - edges (sides) of the triangle.
But what if the triangle has an irregular shape? Two ways are possible here. The first one is to try to divide such a figure into two right-angled triangles, the sum of the areas of which should be calculated separately, and then added. 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 are the sides of the triangle;
C is the angle between these sides.
The latter case is rare in practice, but nevertheless, everything is possible in life, so the above formula will not be superfluous. Good luck in the calculations!