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Triangle Area Calculator

The area of a triangle is the amount of space that is enclosed within the triangle’s three sides. It is a fundamental concept in geometry and is used in various fields such as architecture, engineering, and physics. The formula to calculate the area of a triangle depends on the type of triangle and the information available about it.

Formula:

The general formula to calculate the area of a triangle is:

Area = (base × height) / 2

where the base is any one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.

Different Types of Triangles and their Formulas:

Equilateral Triangle:

An equilateral triangle has all sides equal in length, and each angle measures 60 degrees. The formula to calculate the area of an equilateral triangle is:

Area = (√3 / 4) × side²

where side is the length of any one side of the triangle.

Isosceles Triangle:

An isosceles triangle has two sides equal in length, and the third side is different. The height of an isosceles triangle divides the base into two equal parts. The formula to calculate the area of an isosceles triangle is:

Area = (base × height) / 2

where base is the length of the equal sides and height is the distance from the vertex opposite the base to the base.

Scalene Triangle:

A scalene triangle has all sides of different lengths and no angles are equal. The formula to calculate the area of a scalene triangle is:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides.

Example Problems:

Find the area of an equilateral triangle whose side length is 5 cm.

Solution:

Area = (√3 / 4) × side² = (√3 / 4) × 5² = 10.83 cm²

Therefore, the area of the equilateral triangle is 10.83 cm².

An isosceles triangle has two sides of length 8 cm each and a base of length 10 cm. Find its area.

Solution:

The height of the isosceles triangle can be found using the Pythagorean theorem:

h² = 8² – (10/2)² h² = 36 h = 6 cm

Area = (base × height) / 2 = (10 × 6) / 2 = 30 cm²

Therefore, the area of the isosceles triangle is 30 cm².

Find the area of a scalene triangle with sides of length 5 cm, 7 cm, and 9 cm.

Solution:

The semi-perimeter of the triangle is:

s = (5 + 7 + 9) / 2 = 10.5 cm

Area = √(s(s-a)(s-b)(s-c)) = √(10.5(10.5-5)(10.5-7)(10.5-9)) = 17.99 cm²

Therefore, the area of the scalene triangle is 17.99 cm².

The area of a triangle is a basic concept in geometry and is used in various fields. It can be calculated using different formulas depending on the type of triangle and the information available about it. By understanding the formulas and solving example problems, one can easily calculate the area of any triangle.