Formula for calculating the area of ​​a triangle: right, regular, isosceles, equilateral

What is the formula for calculating the area of ​​a regular, right, and isosceles triangle ? Please refer to the article below to understand the easiest and most commonly used ways to calculate the area of ​​a triangle.

Table of Contents

• 1. Calculate the area of ​​a regular triangle
• 2. Calculate the area of ​​an isosceles triangle
• 3. Calculate the area of ​​an equilateral triangle
• 4. Calculate the area of ​​a right triangle
• 5. Calculate the area of ​​a right isosceles triangle
• 6. Formula for calculating the area of ​​a triangle in the Oxyz coordinate system
• Types of triangles

1. Calculate the area of ​​a regular triangle

Triangle ABC has three sides a, b, c, ha is the height from vertex A as shown:

a. General formula

The area of ​​a triangle is equal to the height multiplied by the length of the opposite side (the base) and divided by 2.

Poem on calculating the area of ​​a regular triangle

The area of ​​a triangle is easy.
Multiply the height by the base and divide it in half.

For example:

Calculate the area of ​​a triangle with a base length of 5m and a height of 24dm.

Solution: Height 24dm = 2.4m

The area of ​​the triangle is:

b. Calculate the area of ​​a triangle when knowing one angle

The area of ​​a triangle is equal to half the product of two adjacent sides times the sine of the angle between those two sides in the triangle.

For example:

Triangle ABC has side BC = 7, side AB = 5, angle B equals 60 degrees. Calculate the area of ​​triangle ABC?

Prize:

c. Calculate the area of ​​a triangle when knowing 3 sides using Heron's formula.

Using the proven Heron formula:

With p being the semi-perimeter of the triangle:

Can be rewritten using the formula:

For example:

Calculate the area of ​​the triangle with side lengths AB = 8, AC = 7, CB = 9

Prize:

The semi-perimeter of triangle ABC is

Applying the hero formula we have

d. Calculate the area using the radius of the circle circumscribing the triangle (R).

Other:

Note: It is necessary to prove that R is the radius of the circle circumscribing the triangle.

For example:

Given triangle ABC, the lengths of the sides are a = 6, b = 7, c = 5, R = 3 (R is the radius of the circle circumscribing triangle ABC). Calculate the area of ​​triangle ABC.

Prize:

e. Calculate the area using the radius of the circle inscribed in the triangle (r).

• p: Half the perimeter of the triangle.
• r: Radius of the inscribed circle.

For example: Calculate the area of ​​triangle ABC knowing the lengths of the sides AB = 20, AC = 21, BC = 15, r = 5 (r is the radius of the circle inscribed in triangle ABC).

Prize:

The semi-perimeter of a triangle is:

r= 5

The area of ​​the triangle is:

2. Calculate the area of ​​an isosceles triangle

Isosceles triangles are like regular triangles, we can apply the formula of multiplying the height by the base, then dividing by 2 as above. In addition, there will be more complex advanced formulas:

Isosceles triangle ABC has three sides, a is the length of the base, b is the length of the two sides, ha is the height from vertex A as shown:

Applying the formula for calculating the area of ​​a regular triangle, we have the formula for calculating the area of ​​an isosceles triangle:

3. Calculate the area of ​​an equilateral triangle

Equilateral triangle ABC has three equal sides, a is the length of the sides as shown:

Applying Heron's theorem to deduce, we have the formula for calculating the area of ​​an equilateral triangle:

4. Calculate the area of ​​a right triangle

Triangle ABC is right-angled at B, a, b are the lengths of the two right-angled sides:

Apply the formula for calculating the area of ​​a right triangle with the height being one of the two right angle sides and the base being the remaining side.

Formula for calculating the area of ​​a right triangle:

Poem on calculating the area of ​​a right triangle:

Triangle with two right angles.
Keep calm, don't panic and make mistakes.

Side, side multiplied, divided by two
is the area, do the exercise quickly

5. Calculate the area of ​​a right isosceles triangle

Triangle ABC is a right-angled triangle at A, a is the length of the two sides:

Applying the formula for calculating the area of ​​a right triangle to the area of ​​an isosceles right triangle with equal height and base, we have the formula:

6. Formula for calculating the area of ​​a triangle in the Oxyz coordinate system

Theoretically, we can use the above formulas to calculate the area of ​​a triangle in space or in Oxyz space. However, this will encounter some difficulties in calculation. Therefore, in Oxyz space, people often calculate the area of ​​a triangle by using the directional product.

In space Oxyz, given triangle ABC. The area of ​​triangle ABC is calculated by the formula:

Example :

In the Oxyz space, given triangle ABC with coordinates of three vertices A(-1;1;2), B(1;2;3), C(3;-2;0). Calculate the area of ​​triangle ABC.

Solution :

We have:

To calculate the area of ​​a triangle, you need to determine what type of triangle it is, from there find the correct area calculation formula and the necessary factors to calculate the area of ​​a triangle as quickly as possible.

Types of triangles

Regular triangle: is the most basic triangle, with different side lengths and different interior angle measures. Regular triangles can also include special cases of triangles.

Isosceles triangle: is a triangle with two equal sides, these two sides are called the two lateral sides. The vertex of an isosceles triangle is the intersection point of the two lateral sides. The angle formed by the vertex is called the apex angle, the other two angles are called the base angles. The property of an isosceles triangle is that the two base angles are equal.

Equilateral triangle: is a special case of an isosceles triangle with all three sides equal. The property of an equilateral triangle is that it has three equal angles and is 60 degrees.

Right triangle: is a triangle with one angle equal to 90 (a right angle).

Obtuse triangle: is a triangle with an interior angle greater than 90 (an obtuse angle) or an exterior angle less than 90 (an acute angle).

Acute triangle: is a triangle with three interior angles all less than 90 (three acute angles) or with all exterior angles greater than 90 (six obtuse angles).

Right isosceles triangle: is both a right triangle and an isosceles triangle.

• Formula for calculating the perimeter of a triangle
• Formula for calculating height in regular, isosceles, equilateral, and right triangles
• What is the centroid? Formula for calculating the centroid of a triangle
• What is a perpendicular bisector?

Above is a summary of common triangle area calculation formulas, calculating triangle area in the oxyz coordinate system. If you have any concerns, questions or contributions, please leave a comment below to discuss with Quantrimang.com.