A triangle is a closed shape made of three straight line segments. It is one of the most basic and important shapes in geometry.

A triangle has six elements:

• 3 sides
• 3 angles

Triangles appear in many mathematical problems and real-life structures such as bridges, roofs, and engineering designs.

Area of a Triangle

The area of a triangle can be found using the formula:

Area = (1/2) × base × height
The base is any side of the triangle.
The height is the perpendicular distance from the base to the opposite vertex.

Example

Find the area of a triangle with base 6 and height 4.

Area = (1/2) × 6 × 4 = 12 square units

Pythagorean Formula

For a right triangle, the relationship between the sides is given by the Pythagorean formula:

c² = a² + b²

Where:

• c is the hypotenuse (the longest side opposite the 90° angle)
• a and b are the other two sides

Example:
Find the hypotenuse of a right triangle with sides 6 and 8.
x² = 6² + 8²
x² = 36 + 64
x² = 100
x = 10
So the missing side is 10.

Interior and Exterior Angles of a Triangle

The sum of the interior angles of a triangle is:

180°

The sum of the exterior angles of a triangle is:

360°

These rules help us find missing angles in triangle problems.

Video Explanation

Practice

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Continue Learning

1. Types of Triangles
2. Triangles (Basics)
3. Sum of Angles of a Triangle is 180° (Proof)
4. Find the Missing Angle of a Triangle
5. Sum of Exterior Angles of a Triangle (Proof)
6. Exterior Angle Theorem of a Triangle
7. Two Exterior Angles at a Vertex are Equal (Proof)
8. Two Exterior Angles are Equal at a Vertex (Quick Proof)

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