Triangles (Basics)

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:

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:

$$\text{Area } = (1/2) \times \text{base } \times \text{height}$$

The base is any side of the triangle.

The height is the perpendicular distance from the base to the opposite vertex.

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

$$\text{Area } = (1/2) \times 6 \times 4 = 12 \text{ square units}$$

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

$$c^2 = a^2 + b^2$$

Where:

Find the hypotenuse of a right triangle with sides $6$ and $8$.

$x^2 = 6^2 + 8^2$
$x^2 = 36 + 64$
$x^2 = 100$
$x = 10$

So the missing side is $10$.

The sum of the interior angles of a triangle is:

$180^\circ$

The sum of the exterior angles of a triangle is:

$360^\circ$

These rules help us find missing angles in triangle problems.