Isosceles Triangle Area

Isosceles Triangle AreaEach student, shirking from his studies, has repeatedly heard from adults that the knowledge gained in the lessons will be useful in adult life, but it was hard to believe in it. Nevertheless, reality often leads us to the fact that we must use the very elementary knowledge of chemistry, physics or geometry, for example, to find the area of ​​an isosceles triangle ...

Isosceles triangle

An isosceles triangle is a geometric figure with two identical sides (equal in length). These two identical sides are called lateral. The remaining third party with excellent length is called the base.

There is also the concept of a regular triangle, in which both sides and base have the same length. The right triangle can also be called isosceles, with the exception that instead of the usual two identical sides, it has three. The converse statement of this fact will be considered incorrect.

Properties

To find the area of ​​an isosceles triangle, it is necessary to know its basic properties.

There are three properties required for computational actions:

  1. Angles that are opposite to the equal sides of a geometric figure are also equal in relation to each other. The bisectors, heights and medians to be drawn from these angles will also be equal.
  2. If we draw a bisector, height, medians and draw the median perpendicular passing through the central point of the base, they will coincide with each other. On this line will lie the centers described and inscribed in a triangle of circles.
  3. The angles on both sides of the base are identical to each other.

Isosceles Triangle Area

How to calculate the area of ​​an isosceles triangle

Find the area of ​​an isosceles triangle using the well-known formula.

Isosceles Triangle Area

To do this, you need to know what is the product of half the base and height.

But what if the height or length of the base is unknown? Let us consider several examples of calculating the unknown components for finding the area of ​​an isosceles triangle.

If you know the length of the base and the length of the side, you can use the Pythagorean theorem (a2 + b2 = c2) to find the height.Since the lateral side is the hypotenuse, and ½ of the base is the leg, you can easily find out the necessary value.

If you know what the length of the base is and how many degrees it makes the angle between the base and the side, this is quite enough to find the area of ​​an isosceles triangle. From the aspect ratio using the formula h = c * ctg (B) / 2, it is necessary to find the height, dividing the side c into two parts. After that you will have all the necessary values.

If you are given the height and the angle between the base and one of the sides, you first need to find the height from the ratio of the two sides of the figure according to the formula c = h * tg (B) * 2. The result will be half the base, therefore, it must be doubled. After that, you can find the area by the formula above.

Isosceles Triangle Area

As you can see, it is not difficult to learn the area of ​​an isosceles triangle, even if you have a minimum amount of information on hand. Not all school knowledge can be useful in life, but in this case, rapid calculations will help you solve the problems of organizing space or consuming materials (construction, creativity, etc.).



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