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How to find the area of an isosceles triangle
The mathematics, and geometry in particular, according to polls of school students, one of the most unloved lessons, and all because force to learn a huge number of formulas which in life of 90% from present adults did not find practical application. But, for a minute, we learn formulas, we solve problems, we do the equations not for this purpose that they can be useful to us in life and therefore as it develops thinking and logic. Still Ancient Greek wise men said that the intelligence of the person can be measured on knowledge of mathematical sciences. And time you decided to examine application of formulas on an isosceles triangle – we get it together and we read article entirely.
Before pristupatk to the answer to a question how to find the area of an isosceles triangle and to pass to practical part of article where formulas and calculations are given, let's designate for ourselves concept. The isosceles triangle is a triangle in which two of three parties which are called lateral are equal on length. In a case with the correct triangle where all parties are equal, it too is considered isosceles, however on the contrary when the isosceles triangle is considered correct – incorrectly.
The parties of a triangle should be designated, we will make it thus as it is given on the picture below where: and – lateral faces, the b-basis, and h-height.
How to calculate the area of an isosceles triangle, formula.
After we made designations of height, the parties and a corner, it is possible to start the solution of a task.
For a start, we will define that we know.
If height and the basis – that approaches a classical formula (*-a multiplication sign):
S = ½ * b*h
Let's substitute, for an example, number, where: h=16, b=18, we receive the following:
S = ½ * 18*16=9*16=144;
The area of an isosceles triangle is S=144 cm2
There are also other formulas which will help us how to learn the area of an isosceles triangle. One of such formulas is Heron's method. Let's not write a difficult formula, we will take, for the basis reduced:
S = ¼ b √4*a2-b2
It is clear that b – the basis, and - the equal parties. The formula approaches in that case when h-height is unknown.
We substitute values, let a=6, b=3, we receive the following:
S = ¼ * 3 √4*62-32 = ¾ √144-9 = ¾ * 9 = 8,7
It is possible to use to calculate the area, the equal parties of a triangle and a corner between the parties:
According to the table of sine the corner in 45o equals 0,7071, the party and let will be equal 6 cm, we receive the following:
As a result, the area of an isosceles triangle it is equal 12,6 cm2.
There are even ways of calculation of the area including in relation to an isosceles triangle, however they are rather difficult and are not applied in "elementary", on concept of difficult mathematics, calculations, like given above. And to speak about things which teachers with an experience will not understand even – is not necessary.
So, it is possible to breathe sigh of relief, on it we will consider a small course of geometry on finding of the area of an isosceles triangle ended, and the knowledge gained as a result of reading of article – acquired on "five".
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