How to find the area and perimeter of a triangle. How to find the area and perimeter of a triangle? Perimeter and area of a triangle

Any triangle is equal to the sum of the lengths of its three sides. The general formula for finding the perimeter of triangles is:

P = a + b + c

where P is the perimeter of the triangle a, b and c- his sides.

It can be found by adding the lengths of its sides in series or by multiplying the length of the side by 2 and adding the length of the base to the product. The general formula for finding the perimeter of isosceles triangles will look like this:

P = 2a + b

where P is the perimeter of an isosceles triangle, a- any of the sides, b- base.

You can find it by adding the lengths of its sides in series or by multiplying the length of any of its sides by 3. The general formula for finding the perimeter of equilateral triangles will look like this:

P = 3a

where P is the perimeter of an equilateral triangle, a- any of its sides.

Square

To measure the area of a triangle, you can compare it with a parallelogram. Consider a triangle ABC:

If you take a triangle equal to it and attach it so that you get a parallelogram, you get a parallelogram with the same height and base as this triangle:

In this case, the common side of the triangles folded together is the diagonal of the formed parallelogram. From the properties of parallelograms, it is known that the diagonal always divides the parallelogram into two equal triangles, which means that the area of each triangle is equal to half the area of the parallelogram.

Since the area of a parallelogram is equal to the product of its base and its height, the area of a triangle will be equal to half of this product. So for Δ ABC area will be equal to

Now consider a right triangle:

Two equal right-angled triangles can be folded into a rectangle if they are leaned against each other by the hypotenuse. Since the area of a rectangle is equal to the product of its adjacent sides, the area of a given triangle is:

From this we can conclude that the area of any right triangle is equal to the product of the legs divided by 2.

From these examples, it can be concluded that the area of any triangle is equal to the product of the length of the base and the height dropped to the base, divided by 2. The general formula for finding the area of triangles will look like this:

S =	ah a
	2

where S is the area of the triangle, a- its foundation h a- height lowered to the base a.

In the proposed task, we are asked to tell how to find the perimeter and area of a triangle. To do this, you need to have an idea of \u200b\u200bwhat a geometric figure is a triangle.

Triangle

In mathematics, a triangle is a geometric figure, which is formed by three segments that connect three points that do not lie on one straight line. Moreover, these points are called the vertices of the triangle, and the segments connecting them are called the sides of the triangle.

Perimeter and area of a triangle

Finding the perimeter of a triangle. To find the perimeter of a triangle, you need to know the length of all its sides. Then the perimeter is found by adding them together.
Finding the area of a triangle given the base and the height. Knowing the base and height of a triangle, we can find its area using the formula:

S = 1/2 * a * h, where a is the base and h is the height.

Finding the area of a triangle given two sides and the angle between them. If we know two sides of a triangle and the angle between them, then we can find its area using the following formula:

S = 1/2 * a * b * sin a (the angle between the sides).

Finding the area of a triangle in terms of its three sides. If we know three sides of a triangle, then we can find its area, for which we first find the perimeter, and then solve using the formula:

S = √(p (p-a) (p-b) (p-c)).

Thus, we examined the geometric figure of a triangle, the formula for finding its perimeter and all possible formulas for finding its area.

A triangle is a two-dimensional figure with three edges and the same number of vertices. It is one of the basic shapes in geometry. An object has three angles, their total degree measure is always 180°. Vertices are usually denoted by Latin letters, for example, ABC.

Theory

Triangles can be classified according to different criteria.

If the degree measure of all its angles is less than 90 degrees, then it is called acute-angled, if one of them is equal to this value - rectangular, and in other cases - obtuse-angled.

When a triangle has all sides of the same size, it is called an equilateral triangle. In the figure, this is marked with a mark perpendicular to the segment. The angles in this case are always 60°.

If only two sides of a triangle are equal, then it is called isosceles. In this case, the angles at the base are equal.

A triangle that does not fit the two previous options is called a scalene triangle.

When two triangles are said to be equal, it means they are the same size and shape. They also have the same angles.

If only degree measures coincide, then the figures are called similar. Then the ratio of the corresponding sides can be expressed by a certain number, which is called the coefficient of proportionality.

Perimeter of a triangle in terms of area or sides

As with any polygon, the perimeter is the sum of the lengths of all sides.

For a triangle, the formula looks like this: P = a + b + c, where a, b and c are the lengths of the sides.

There is another way to solve this problem. It consists in finding the perimeter of a triangle through the area. First you need to know the equation that relates these two quantities.

S = p × r, where p is the semi-perimeter and r is the radius of the circle inscribed in the object.

It is quite easy to transform the equation into the form we need. We get:

Do not forget that the real perimeter will be 2 times larger than the received one.

That's how simple examples are solved.

How to find the area of a triangle knowing the perimeter and side? and got the best answer

Answer from Alexander Bezrukov[guru]
if the side is 85 then the bottom is 338-85*2. divide in half, here you have two right-angled triangles in which the leg of the leg and the hypotenuse are known, knowing them you will find the second leg, and from here the area
Alexander Bezrukov
Thinker
(7636)
I can but I won't. think by yourself. I can give advice, but I can't decide for you. meaning that the area of such a triangle is equal to the height multiplied by the base. we will find the base, knowing the perimeter and two sides 338-85-85 = count for yourself.
but the height is a leg in a triangle (draw a vertically divided triangle on paper and you will understand everything) with a hypotenuse of 85 and a leg base / 2
understood?

Answer from 2 answers[guru]

Hey! Here is a selection of topics with answers to your question: How to find the area of a triangle knowing the perimeter and side?

Answer from Divergent[guru]
If isosceles, then simply. You find the base (338-2*85)=168. And then there are two ways - you can use the Heron formula, or you can find the height lowered to the base. In an isosceles triangle, such a height is also a median, therefore it divides the base in half into segments 168/2=84 cm long. Find the height using the Pythagorean theorem: h=sqrt(85^2-84^2)=sqrt(169)=13. So, the area of the triangle is 13*168/2=1092, that's all!