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Geometry class 10 || Area of Triangle & Quadrilateral ||


All about Triangle and Quadrilateral

A triangleis a three-sided polygon one of the simplest and most fundamental shapes in geometry. It consists of three edges (sides) and three vertices (corners). The sum of the interior angles of any triangle is always 180 degrees.

#Types of Triangles:
Triangles can be classified based on their sides and angles:

#### 1.Based on Sides:
Equilateral Triangle: All three sides are of equal length, and all interior angles are 60 degrees.
**Isosceles Triangle: Two sides are of equal length, and the angles opposite those sides are equal.
Scalene Triangle: All three sides have different lengths, and all three interior angles are different.

#2. Based on Angles:
Acute Triangle: All three angles are less than 90 degrees.
Right Triangle: One of the angles is exactly 90 degrees.
Obtuse Triangle: One of the angles is greater than 90 degrees.

Properties of a Triangle:
Vertices: The three points where the sides meet are called the vertices.
Altitude: The perpendicular distance from a vertex to the opposite side.
Perimeter: The sum of the lengths of the three sides.

Triangles are important in mathematics and other fields because of their simple yet versatile properties, appearing in a wide range of problems in geometry, trigonometry, physics, and engineering.

similarly
A quadrilateral is a polygon with four sides (edges) four vertices (corners) and four angles. The sum of the interior angles of any quadrilateral is always 360° degrees.

Types of Quadrilaterals:
Quadrilaterals can be classified into several categories based on the properties of their sides and angles:

1. Parallelogram:
Opposite sides are parallel and equal in length.
Opposite angles are equal.
Diagonals bisect each other.

2.Rectangle:
A special type of parallelogram where all angles are 90 degrees.
Opposite sides are equal, and diagonals are equal in length.

3. Square:
A special type of rectangle where all sides are of equal length.
All angles are 90 degrees, and diagonals are equal and bisect each other at right angles.

4. Rhombus
A parallelogram with all sides of equal length.
Opposite angles are equal, and diagonals bisect each other at right angles but are not necessarily equal in length.

5. Trapezium (Trapezoid in the U.S.):
A quadrilateral with one pair of opposite sides that are parallel (called bases).
The non-parallel sides are called legs.

6. Kite:
A quadrilateral with two pairs of adjacent sides that are equal.
One pair of opposite angles is equal, and the diagonals intersect at right angles, with one diagonal bisecting the other.

Properties of a Quadrilateral:
Vertices: The four points where the sides meet.
Sides: The four edges connecting the vertices.

Diagonals: Line segments connecting opposite vertices.

Perimeter: The total length of all four sides.

Area: The space enclosed by the quadrilateral, which depends on the type and can be calculated using various formulas.

Quadrilaterals are a fundamental part of geometry and appear frequently in architecture, art, and many other practical applications due to their flexibility and the wide range of shapes they can form.