How to find the area of an isosceles triangle
Mathematics, and geometry in particular, according topolls of schoolchildren, one of the most unloved lessons, and all because they make you learn a huge number of formulas that in life 90% of current adults have not found practical application. But, for a minute, we learn formulas, solve problems, make equations not for the fact that they can be useful to us in life, but because it develops thinking and logic. Even the ancient Greek sages said that the human intellect can be measured by the knowledge of mathematical sciences. And since you decided to get acquainted with the application of the formulas for an isosceles triangle - we take ourselves in hand and read the entire article.
Before you start to answer the question how to findthe area of an isosceles triangle and go to the practical part of the article, where formulas and calculations are given, let us denote the very concept for ourselves. An isosceles triangle is a triangle in which two of the three sides are equal in length, called lateral sides. In the case of a regular triangle, where all sides are equal, it is also considered isosceles, but vice versa, when an isosceles triangle is considered correct - is false.
The sides of the triangle should be designated, we will do it this way, as shown in the picture below, where: a - sides, b-base, and h-height.
How to calculate the area of an isosceles triangle, formulas.
After we have made the notation of height, sides and angle, we can begin to solve the problem.
To begin with, we will determine what we know.
If the height and the bottom - then the classical formula (* - multiplication sign):
S = ½ * b * h
Let's substitute, for example, the numbers where: h = 16, b = 18, we get the following:
S = ½ * 18 * 16 = 9 * 16 = 144;
The area of an isosceles triangle is S = 144 cm2
There are other formulas that will help usin how to know the area of an isosceles triangle. One such formula is Heron's method. Let's not write a complex formula, we take, for a basis, a shortened:
S = ¼ b √4 * a2-b2
It is clear that b is the basis, and - equal sides. The formula is suitable in the case where h-height is unknown.
Substituting the values, let a = 6, b = 3, we get the following:
S = ¼ * 3 √4 * 62-32 = ¾ √144-9 = ¾ * 9 = 8,7
You can use to calculate the area equal to the sides of the triangle and the angle between the sides:
According to the sine table, the angle at 45 ° equals 0.7071, the side a and let it be 6 cm, we obtain the following:
As a result, the area of an isosceles triangle is 12.6 cm2.
There are also ways to calculate the area, includingincluding in the case of an isosceles triangle, but they are rather complicated and do not apply to "elementary" calculations, such as those given above, in the notion of complex mathematics. And it's not worth talking about things that even teachers with experience will not understand.
So, you can breathe a sigh of relief, on thisa small course of geometry for finding the area of an isosceles triangle will be considered complete, and the knowledge obtained as a result of reading the article is learned by "five".
