How to find the area of a triangle

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

Remembering geometry: formulas for arbitrary, rectangular, isosceles and equilateral figures.

How to find the area of any triangle

You can calculate the area of a triangle in different ways. Choose a formula depending on the quantities you know.

Knowing the side and the height

1. Multiply the side of the triangle by the height drawn to that side.
2. Divide the result by two.

• S is the required area of the triangle.
• a - side of the triangle.
• h is the height of the triangle. This is a perpendicular dropped to the side or its extension from the opposite vertex.

Knowing the two sides and the angle between them

1. Count the product of the two known sides of the triangle.
2. Find the sine of the angle between the selected sides.
3. Multiply the numbers you get.
4. Divide the result by two.

• S is the required area of the triangle.
• a and b are the sides of the triangle.
• α is the angle between sides a and b.

Knowing the three sides (Heron's formula)

1. Calculate the differences between the half-perimeter of the triangle and each of its sides.
2. Find the product of the numbers obtained.
3. Multiply the result by a semi-perimeter.
4. Find the root of the resulting number.

• S is the required area of the triangle.
• a, b, c - sides of the triangle.
• p - half-perimeter (equal to half of the sum of all sides of the triangle).

Knowing the three sides and the radius of the circumscribed circle

1. Find the product of all sides of the triangle.
2. Divide the result by the four radii of the circle around the rectangle.

• S is the required area of the triangle.
• R is the radius of the circumscribed circle.
• a, b, c - sides of the triangle.

Knowing the radius of the inscribed circle and the semi-perimeter

Multiply the radius of the circle inscribed in the triangle by the semi-perimeter.

• S is the required area of the triangle.
• r is the radius of the inscribed circle.
• p - half-perimeter of a triangle (equal to half of the sum of all sides).

How to find the area of a right triangle

1. Count the product of the legs of the triangle.
2. Divide the result by two.

• S is the required area of the triangle.
• a, b - the legs of the triangle, that is, the sides that intersect at right angles.

How to find the area of an isosceles triangle

1. Multiply the base by the height of the triangle.
2. Divide the result by two.

• S is the required area of the triangle.
• a is the base of the triangle. This is the side that is not equal to the other two. Recall that in an isosceles triangle, two of the three sides have the same length.
• h is the height of the triangle. It is a perpendicular dropped to the base from the opposite vertex.

How to find the area of an equilateral triangle

1. Multiply the square of the side of the triangle by the root of three.
2. Divide the result by four.

• S is the required area of the triangle.
• a - side of the triangle. Recall that in an equilateral triangle, all sides have the same length.