Sometimes in life there are situations when it is necessary to delve into the memory in search of long-forgotten school knowledge.For example, you need to determine the area of land or a triangular shape came the next repair in an apartment or private home, and you need to calculate how much material will go to the surface with a triangular shape.There was a time when you could solve this puzzle for a couple of minutes, and is now desperately trying to remember how to determine the area of a triangle?
not necessary because of this experience!After all, it is quite normal that the human brain decides to shift long-unused knowledge somewhere in a remote corner, from which they are sometimes not so easily removed.You do not have to suffer with the search for the forgotten school knowledge to solve this problem, this article contains a variety of methods that make it easy to find the desired area of the triangle.
is well known that this kind of triangle is called a polygon, which is limited to the minimum possible number of sides.In principle, any polygon can be divided into several triangles, line segments connecting the vertices that do not cross him.Therefore, knowing the formula for calculating the area of a triangle, you can calculate the area of virtually any shape.
among all possible triangles that occur in life, the following special types: equilateral, isosceles and rectangular.
easiest area of the triangle is calculated when one of its angles is right, that is, in the case of a right triangle.It is easy to notice that he is half of the rectangle.Therefore, an area equal to half the product of the sides that form a right angle to each other.
If we know the height of the triangle dropped from one of its vertices on the opposite side, and the length of this side, which is called the base, the area is calculated as the product of half the height of the base.Write it down using a formula:
S = 1/2 * b * h, which
S - the desired area of the triangle;
b, h -, respectively, and the height of the base of the triangle.
so easy to calculate the area of an isosceles triangle, since the height will divide the opposite side of the half, and it can easily be measured.If it is determined the area of a right triangle, the height as convenient to take the length of one side, forming a right angle.
Everything is nice, but how to determine whether one of the corners of the triangle straight or not?If the size of our small figures, you can use the building corner, the drawing triangle, cards or other object with a rectangular shape.
But what if we have a triangular plot of land?In this case, proceed as follows: count from the top prospective right angle on one side away fold 3 (30 cm, 90 cm, 3 m), and on the other side of metered proportionately distance multiple of 4 (40 cm and 160 cm,4 m).Now you need to measure the distance between the endpoints of these two segments.If you got the value multiples of 5 (50 cm, 250 cm, 5 m), it can be argued that the angle of the line.
If you know the length of each of the three sides of our figure, the area of a triangle can be determined using the formula of Heron.In order to have a more simple look, use a new value, which is called semiperimeter.It is the sum of all sides of our triangle, divided in half.After semiperimeter counted, you can begin to determine the area of the formula:
S = sqrt (p (pa) (pb) (pc)), where
sqrt - square root;
p - value semiperimeter (p = (a + b + c) / 2);
a, b, c - 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 this figure by two right-angled triangles, the sum of the areas that count separately and then added together.Or, if you know the angle between the two sides and the size of these sides, apply the formula:
S = 0.5 * ab * sinC, where
a, b - side of the triangle;
with - the angle between the parties.
latter case, the practice is rare, but nonetheless, in life everything is possible, so the above formula will not be superfluous.Good luck in your calculations!
