Formula to calculate the area of ​​a triangle: square, regular, balanced, and even

There are many different ways to calculate the area of ​​a triangle with many commonly used formulas as well as formulas when used should be proved. In this article, TipsMake.com will introduce you to the most understandable and used triangle area calculation methods so you can apply immediately in the exam.

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 1

Types of triangles

Ordinary triangle : is the most basic triangle, with different lengths of sides, measurement of internal angles is also different. Common triangles can also include special cases of triangles.

Weight triangle : is a triangle with two equal sides, these two sides are called two sides. The top of an isosceles triangle is the intersection of the two sides. The angle created by the vertex is called the angle at the top, the other two corners are called the bottom angle. The properties of the isosceles triangle are equal to the bottom two corners

Equilateral triangle: is a special case of an isosceles triangle with all three sides equal. The properties of an equilateral triangle are equal to and equal to 60 Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 2

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 3

Square triangle : is a triangle with an angle equal to 90 Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 4 (is the right angle).

Prison triangle : is a triangle with a larger inner angle greater than 90 Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 5 (an obtuse angle) or a corner outside of the 90 Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 6 (a sharp angle).

Pointed triangle : is a triangle with three inner angles less than 90 Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 7 (three sharp corners) or have all the outer corners greater than 90 Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 8 (six corners)

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 9

Square-shaped triangle: both a right triangle and an isosceles triangle.

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 10

Triangle area formula

1. Calculate the area of ​​the regular triangle

Triangle ABC has three sides a, b, c, h _a is the high line from vertex A as shown:

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 11

a. General formula

The area of ​​the triangle is equal to ½ the product of the lower height from the top with the length of the opposite edge of that vertex.

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 12

b. Calculate the triangle area when knowing an angle

The area of ​​the triangle is equal to ½ of the product two adjacent to the sine of the right angle by the two sides in the triangle.

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 13

c. Calculate the area of ​​the triangle when you know the 3 sides by the formula Heron.

Use the proven Heron formula:

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 14

With p is the circumference of the triangle:

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 15

Can be rewritten by the formula:

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 16

d. Calculate the area by the radius of the circumcircle of the triangle (R).

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 17

Different ways: Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 18

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

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

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 19

2. Calculate the area of ​​the isosceles triangle

The triangle of triangle ABC has three sides, a is the length of the bottom edge, b is the length of the two sides, h is the height from the top A as shown:

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 20

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

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 21

3. Calculate the area of ​​the equilateral triangle

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

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 22

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

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 23

4. Calculate the area of ​​the right triangle

The square ABC triangle at B, a, b is the length of two sides of the right angle:

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 24

Applying the formula to calculate the area usually for the area of ​​a right triangle with a height of 1 in 2 right-angled edges and the bottom edge is the other side.

Formula to calculate the area of ​​a right triangle:

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 25

5. Area square triangle weight

The triangle ABC is square in weight at A, a is the length of two sides of the right angle:

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 26

Applying the formula to calculate the area of ​​a right triangle for the area of ​​a square triangle with equal height and edge, we have the formula:

Formula to calculate the area of ​​a triangle: square, regular, balanced, and even Picture 27

Above is the synthesis of common triangle area calculation formulas. If you have any questions or suggestions, please leave a comment below to discuss with TipsMake.com.