Quant Study Notes: Area & Polygons

Polygon and quadrilateral's properties

1.      Polygon: – It is a closed plane figure bounded by three or more than three straight lines.
 There are of two types of polygons.

Convex:       A polygon in which none of its interior angle is more than 180°
Concave:             A polygon in which at least one interior angle is more than 180°.

       Regular Polygon: All the sides are equal and also all the interior angles are equal
Sum of Interior angles of a polygon = (n – 2) × 180
 number of sides

Sum of exterior angle = 360

2. Rectangle: –
  • In a parallelogram with two adjacent angles A and B equal to each other, then the parallelogram is a rectangle or a square.
  •  Diagonals are equal and bisect each other, but not necessarily at right angles.
  • For the given perimeter of rectangle, a square has maximum area.
  • The figure farmed by joining the mid-points of the adjacent sides of rectangle is a rhombus.
  • The quadrilateral formed by joining the mid points of intersections of the angle bisectors of a parallelogram is a rectangle.

3.    Rhombus: –
  •  A parallelogram in which all sides are equal is called a rhombus.
  •  Diagonal of rhombus bisect each other at right angles, but they are not necessarily equal.
  •  Diagonal bisect the vertex angles.
  •   Sum of any two adjacent angles is 180°
  •   Figure formed by joining the mid-points of the adjacent sides of a rhombus is a rectangle

4.  Parallelogram: –
  •  Opposite sides are parallel and equal.
  •  Opposite angles are equal.
  •  Sum of any two adjacent angles is 180°.
  •  Each diagonal divides a parallelogram into two congruent triangles.
  •  The parallelogram that inscribed in a circle is a rectangle.
  •  The parallelogram that circumcircle a circle is a rhombus

5. Trapezium: –
       A quadrilateral whose only one pair of sides is parallel and other two sides are not parallel.

Area of different geometric figures