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.

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

Square triangle : is a triangle with an angle equal to 90

(is the right angle).

Prison triangle : is a triangle with a larger inner angle greater than 90

(an obtuse angle) or a corner outside of the 90

(a sharp angle).

Pointed triangle : is a triangle with three inner angles less than 90

(three sharp corners) or have all the outer corners greater than 90

(six corners)

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

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:

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.

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.

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

Use the proven Heron formula:

With p is the circumference of the triangle:

Can be rewritten by the formula:

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

Different ways:

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).

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:

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

3. Calculate the area of ​​the equilateral triangle

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

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

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:

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:

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:

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:

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.